قائمة الثوابت الرياضية

الثابت الرياضي هو رقم، له دلالة خاصة في العمليات الحسابية. على سبيل المثال، الثابت الرياضي باي (π) يعني نسبة طول محيط الدائرة إلى قطرها. هذه القيمة ثابته لا تتغير لأي دائرة.

بيانات الجدول

• القيمة العددية للثابت: من المراجع العالمية كموقع ماثوورلد أو من موسوعة المتتاليات الصحيحة على الإنترنت والتي تعرف اختصارا باسم أويس ويكي (OEIS).
• لاتخ: الصيغة في تنسيق تخ.
• الصيغة الرياضية: المستخدمة في برنامج ولفرام ألفا.
• أويس: موسوعة على الإنترنت عن الأعداد الصحيحة.
• الكسر المستمر: وهو الكسر الذي يأخذ الصيغة التالية

$x=a_{0}+{\cfrac {1}{a_{1}+{\cfrac {1}{a_{2}+{\cfrac {1}{a_{3}+{\cfrac {1}{\ddots \,}}}}}}}}$

• العام: عام اكتشاف الثابت.
• تنسيق الويب: القيمة بشكل مناسب على صفحات الإنترنت.
• النوع: نوع العدد.
  • ك: عدد كسري
  • غ.ك: عدد غير نسبي (عدد غير كسري)
  • ج : عدد جبري
  • م : عدد متسام
  • خ : عدد مركب

جدول الدوال والثوابت الرياضية

هذا الجدول يهتم بأهم الدوال والثوابت الرياضية على مر العصور:

القيمة العددية	الاسم	الرسومات	الرمز	لاتخ	الصيغة	النوع	أويس ويكي	الكسر المستمر	العام	تنسيق الويب
0.74048048969306104116	ثابت هيرميت تعبئة الكرات بنظام ثلاثي الأبعاد حدسية كيبلر		${\mu _{_{K}}}$	${\frac {\pi }{3{\sqrt {2}}}}{\color {white}......\color {black}}$ أثبت توماس هيلز في عام 2014 أن حدثية كيبلر صحيحة.	pi/(3 sqrt(2))		A093825	[0;1,2,1,5,1,4,2,2,1,1,2,2,2,6,1,1,1,5,2,1,1,1, ...]	1611	0.74048048969306104116931349834344894
22.45915771836104547342	pi^e		$\pi ^{e}$	$\pi ^{e}$	pi^e		A059850	[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]		22.4591577183610454734271522045437350
2.80777024202851936522	ثابت فرانسين روبنسون		${F}$	$\int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	N[int[0 to ∞] {1/Gamma(x)}]		A058655	[2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...]	1978	2.80777024202851936522150118655777293
1.305686729 ≈ بواسطة توماس ودهار 1.305688 ≈ بواسطة ماكمولين	الهندسة الكسيرية لأبلونيوس البرغاوي  ·		$\varepsilon$				A052483	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]	1994 1998	1.305686729 ≈ 1.305688 ≈
0.43828293672703211162 0.360592471871385485 i	الأس الانهائي للوحدة التخليلةi		${}^{\infty }{i}$	$\lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}$	i^i^i^i^i^i^...	خ	A077589  A077590	[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] + [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i		0.43828293672703211162697516355126482 + 0.36059247187138548595294052690600 i
0.9288358271	مجموع مقلوب الأعداد الأولية التوأم		$B_{1}$	${\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{18}}+{\frac {1}{30}}+{\frac {1}{42}}+{\frac {1}{60}}+{\frac {1}{72}}+\cdots$	1/4 + 1/6 + 1/12 + 1/18 + 1/30 + 1/42 + 1/60 + 1/72 + ...		A241560	[0; 1, 13, 19, 4, 2, 3, 1, 1]	2014	0.928835827131
0.63092975357145743709	مجموعة كانتور		$d_{f}(k)$	$\lim _{\varepsilon \to 0}{\frac {\log N(\varepsilon )}{\log(1/\varepsilon )}}={\frac {\log 2}{\log 3}}$	log(2)/log(3) N[3^x=2]	م	A102525	[0;1,1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]		0.63092975357145743709952711434276085
0.31830988618379067153	مقلوب باي (π), سرينفاسا أينجار رامانجن		${\frac {1}{\pi }}$	${\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!\,(1103+26390\;n)}{(n!)^{4}\,396^{4n}}}$	2 sqrt(2)/9801 * Sum[n=0 to ∞] {((4n)!/n!^4) *(1103+ 26390n) / 396^(4n)}	م	A049541	[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]		0.31830988618379067153776752674502872
0.28878809508660242127	فلاجوليت وريتشموند		${Q}$	$\prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)...$	prod[n=1 to ∞] {1-1/2^n}		A048651	[0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1,...]	1992	0.28878809508660242127889972192923078
1.53960071783900203869	ثابت إليوت هرشل ليب للجليد (يستخدم في تحديد عدد المسارات الاويلرية)		${W}_{2D}$	$\lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}$	(4/3)^(3/2)	ج	A118273	[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]	1967	1.53960071783900203869106341467188655
0.20787957635076190854	$i^{i}$		$i^{i}$	$e^{-{\frac {\pi }{2}}}$	e^(-π/2)	م	A049006	[0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...]	1746	0.20787957635076190854695561983497877
4.53236014182719380962	ثابت فان دير باو		${\alpha }$	${\frac {\pi }{\ln(2)}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-\cdots }{{\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots }}$	π/ln(2)		A163973	[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]		4.53236014182719380962768294571666681
0.76159415595576488811	دالة زائدية للعدد 1		${th}\,1$	$-i\tan(i)={\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}$	(e-1/e)/(e+1/e)	م	A073744	[0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...] = [0;2p+1], p∈ℕ		0.76159415595576488811945828260479359
0.59017029950804811302	ثابت تشيبيشيف  ·		${\lambda _{Ch}}$	${\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}={\frac {4({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}$	(Gamma(1/4)^2) /(4 pi^(3/2))		A249205	[0;1,1,2,3,1,2,41,1,6,5,124,5,2,2,1,1,6,1,2,...]		0.59017029950804811302266897027924429
0.07077603931152880353 0.6840003894379-	MKB ثابت  ·  ·		$M_{I}$	$\lim _{n\rightarrow \infty }\int _{1}^{2n}(-1)^{x}~{\sqrt[{x}]{x}}~dx=\int _{1}^{2n}e^{i\pi x}~x^{1/x}~dx$	lim_(2n->∞) int[1 to 2n] {exp(i*Pi*x)*x^(1/x) dx}	خ	A255727  A255728	[0;14,7,1,2,1,23,2,1,8,16,1,1,3,1,26,1,6,1,1, ...] - [0;1,2,6,13,41,112,1,25,1,1,1,1,3,13,2,1, ...] i	2009	0.07077603931152880353952802183028200 -0.68400038943793212918274445999266 i
1.259921049894873164767	الجذر التكعيبي للرقم 2		${\sqrt[{3}]{2}}$	${\sqrt[{3}]{2}}$	2^(1/3)	ج	A002580	[1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,...]		1.25992104989487316476721060727822835
1.09317045919549089396	ثابت سمراندش 1ª		${S_{1}}$	$\sum _{n=2}^{\infty }{\frac {1}{\mu (n)!}}{\color {white}....\color {black}}$ حيث μ(n) هو دالة كيمبنر			A048799	[1;10,1,2,1,2,1,13,3,1,6,1,2,11,4,6,2,15,1,1,...]		1.09317045919549089396820137014520832
0.62481053384382658687 + 1.30024 25902 20120 419 i	الكسر المستمر المعمم للوحدة التخليلية i		${{F}_{CG}}_{(i)}$	$\textstyle i{+}{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+i{/...}}}}}}}}}}}}}={\sqrt {\frac {{\sqrt {17}}-1}{8}}}+i\left({\tfrac {1}{2}}{+}{\sqrt {\frac {2}{{\sqrt {17}}-1}}}\right)$	i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( i+i/(i+i/(i+i/(i+i/(i+i/( ...)))))))))))))))))))))	ج	A156590  A156548	[i;1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,..] = [0;1,i]		0.62481053384382658687960444744285144 + 1.30024259022012041915890982074952 i
3.05940740534257614453	ثابت المضروب المزدوج		${C_{_{n!!}}}$	$\sum _{n=0}^{\infty }{\frac {1}{n!!}}={\sqrt {e}}\left[{\frac {1}{\sqrt {2}}}+\gamma ({\tfrac {1}{2}},{\tfrac {1}{2}})\right]$	Sum[n=0 to ∞]{1/n!!}		A143280	[3;16,1,4,1,66,10,1,1,1,1,2,5,1,2,1,1,1,1,1,2,...]		3.05940740534257614453947549923327861
5.97798681217834912266	ثابت ماديلونغ		${H}_{2}(2)$	$\pi \ln(3){\sqrt {3}}$	Pi Log[3]Sqrt[3]		A086055	[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]		5.97798681217834912266905331933922774
0.91893853320467274178	صيغة راب		${\zeta '(0)}$	$\int \limits _{a}^{a+1}\log \Gamma (t)\,\mathrm {d} t={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0$	integral_a^(a+1) {log(Gamma(x))+a-a log(a)} dx		A075700	[0;1,11,2,1,36,1,1,3,3,5,3,1,18,2,1,1,2,2,1,1,...]		0.91893853320467274178032973640561763
2.20741609916247796230	مسألة الأريكة المتحركة		${S_{_{H}}}$	${\frac {\pi }{2}}+{\frac {2}{\pi }}\,$	pi/2 + 2/pi	م	A086118	[2;4,1,4,1,1,2,5,1,11,1,1,5,1,6,1,3,1,1,1,1,7,...]	1967	2.20741609916247796230685674512980889
1.17628081825991750654	عدد سالم، تخيل ليمير		${\sigma _{_{10}}}$	$x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1$	x^10+x^9-x^7-x^6 -x^5-x^4-x^3+x+1	ج	A073011	[1;5,1,2,17,1,7,2,1,1,2,4,7,2,2,1,1,15,1,1, ...	1983?	1.17628081825991750654407033847403505
0.37395581361920228805	ثابت إميل أرتين		${C}_{Artin}$	$\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)\quad p_{n}\scriptstyle {\text{ = prime}}$	Prod[n=1 to ∞] {1-1/(prime(n) (prime(n)-1))}		A005596	[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]	1999	0.37395581361920228805472805434641641
0.42215773311582662702	حجم رباعي الأسطح		${V_{_{R}}}$	${\frac {s^{3}}{12}}(3{\sqrt {2}}-49\,\pi +162\,\arctan {\sqrt {2}})$	(3*Sqrt[2] - 49*Pi + 162*ArcTan[Sqrt[2]])/12		A102888	[0;2,2,1,2,2,7,4,4,287,1,6,1,2,1,8,5,1,1,1,1, ...]		0.42215773311582662702336591662385075
2.82641999706759157554	ثابت موراتا		${C_{m}}$	$\prod _{n=1}^{\infty }{\underset {p_{n}:\,{prime}}{{\Big (}1+{\frac {1}{(p_{n}-1)^{2}}}{\Big )}}}$	Prod[n=1 to ∞] {1+1/(prime(n) -1)^2}		A065485	[2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28,...]		2.82641999706759157554639174723695374
1.09864196439415648573	ثابت باريس		$C_{Pa}$	$\prod _{n=2}^{\infty }{\frac {2\varphi }{\varphi +\varphi _{n}}}\;,\;\varphi {=}{Fi}$  con  $\varphi _{n}{=}{\sqrt {1{+}\varphi _{n{-}1}}}$   y   $\varphi _{1}{=}1$			A105415	[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]		1.09864196439415648573466891734359621
2.39996322972865332223 بالراديان	الزاوية الذهبية		${b}$	$(4-2\,\Phi )\,\pi =(3-{\sqrt {5}})\,\pi$ = 137.5077640500378546 ...°	(4-2*Phi)*Pi	م	A131988	[2;2,1,1,1087,4,4,120,2,1,1,2,1,1,7,7,2,11,...]	1907	2.39996322972865332223155550663361385
1.64218843522212113687	ثابت ليبيسج		${L2}$	${\frac {1}{5}}+{\frac {\sqrt {25-2{\sqrt {5}}}}{\pi }}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\left|\sin({\frac {5t}{2}})\right|}{\sin({\frac {t}{2}})}}\,dt$	1/5 + sqrt(25 - 2*sqrt(5))/Pi	م	A226655	[1;1,1,1,3,1,6,1,5,2,2,3,1,2,7,1,3,5,2,2,1,1,...]	1910	1.64218843522212113687362798892294034
1.26408473530530111307	ثابت فارديt		${V_{c}}$	${\frac {\sqrt {3}}{\sqrt {2}}}\prod _{n\geq 1}\left(1+{1 \over (2e_{n}-1)^{2}}\right)^{\!1/2^{n+1}}$			A076393	[1;3,1,3,1,2,5,54,7,1,2,1,2,3,15,1,2,1,1,2,1,...]	1991	1.26408473530530111307959958416466949
1.5065918849 ± 0.0000000028	مساحة مجموعة ماندلبرو		$\gamma$	${\sqrt {6\pi -1}}-e=1.506591651\cdots$			A098403	[1;1,1,37,2,2,1,10,1,1,2,2,4,1,1,1,1,5,4,...]	1912	1.50659177 +/- 0.00000008
1.6111149258083	ثابت المضروب الأسي		${S_{Ef}}$	$\sum _{n=1}^{\infty }{\frac {1}{n^{(n{-}1)^{\cdot ^{\cdot ^{\cdot ^{2^{1}}}}}}}}=1{+}{\frac {1}{2^{1}}}{+}{\frac {1}{3^{2^{1}}}}+{\frac {1}{4^{3^{2^{1}}}}}+{\frac {1}{5^{4^{3^{2^{1}}}}}}{+}\cdots$		م	A080219	[1; 1, 1, 1, 1, 2, 1, 808, 2, 1, 2, 1, 14,...]		1.61111492580837673611111111111111111
1.11786415118994497314	ثابت جوه شموتز		$C_{GS}$	$\int _{0}^{\infty }{\frac {\log(s+1)}{e^{s}-1}}\ ds=\!-\!\sum _{n=1}^{\infty }{\frac {e^{n}}{n}}Ei(-n)$	Integrate{ log(s+1) /(E^s-1)}		A143300	[1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1,...]		1.11786415118994497314040996202656544
0.3181315052047641 ±1.337235701430689	النقط الثابتة على اللوغاريتم الأكبر ·		${-W(-1)}$	$\lim _{n\rightarrow \infty }$$f(x)=\underbrace {\log(\log(\log(\log(\cdots \log(\log(x))))))\,\!} \atop {\log _{s}{\text{ n times}}}$ تختلف القيمة الابتدائية لx لتصبح ${\textstyle 0,1,e,e^{e},e^{e^{e}}}$, etc.	-W(-1)	خ	A059526  A059527	[-i;1 +2i,1+i,6-i,1+2i,-7+3i,2i,2,1-2i,-1+i,-, ...]		0.31813150520476413531265425158766451 -1.33723570143068940890116214319371 i
0.28016949902386913303	ثابت بيرنشتين		${\beta }$	$\approx {\frac {1}{2{\sqrt {\pi }}}}$	1/(2 sqrt(pi))	م	A073001	[0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1,...]	1913	0.28016949902386913303643649123067200
0.66016181584686957392	ثابت العددان الأوليان التوأمان		${C}_{2}$	$\prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}$	prod[p=3 to ∞] {p(p-2)/(p-1)^2		A005597	[0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...]	1922	0.66016181584686957392781211001455577
1.22674201072035324441	ثابت معامل فيبوناتشي		$F$	$\prod _{n=1}^{\infty }\left(1-\left(-{\frac {1}{{\varphi }^{2}}}\right)^{n}\right)=\prod _{n=1}^{\infty }\left(1-\left({\frac {{\sqrt {5}}-3}{2}}\right)^{n}\right)$	prod[n=1 to ∞] {1-((sqrt(5) -3)/2)^n}		A062073	[1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23,...]		1.22674201072035324441763023045536165
0.11494204485329620070	ثابت كيبلر-بووكمب		${\rho }$	$\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...$	prod[n=3 to ∞] {cos(pi/n)}		A085365	[0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...]		0.11494204485329620070104015746959874
1.78723165018296593301	ثابت كومورنيك-لوريتي		${q}$	$1=\!\sum _{n=1}^{\infty }{\frac {t_{k}}{q^{k}}}\qquad \scriptstyle {\text{Raiz real de}}\displaystyle \prod _{n=0}^{\infty }\!\left(\!1{-}{\frac {1}{q^{2^{n}}}}\!\right)\!{+}{\frac {q{-}2}{q{-}1}}=0$	FindRoot[(prod[n=0 to ∞] {1-1/(x^2^n)}+(x-2) /(x-1))= 0, {x, 1.7}, WorkingPrecision->30]	م	A055060	[1;1,3,1,2,3,188,1,12,1,1,22,33,1,10,1,1,7,...]	1998	1.78723165018296593301327489033700839
3.30277563773199464655	القيمة البرونزية		${\sigma }_{\,Rr}$	${\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}$	(3+sqrt 13)/2	ج	A098316	[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...] = [3;3,...]		3.30277563773199464655961063373524797
0.82699334313268807426	تغطية القرص		${C_{5}}$	${\frac {1}{\sum \limits _{n=0}^{\infty }{\frac {1}{\binom {3n+2}{2}}}}}={\frac {3{\sqrt {3}}}{2\pi }}$	3 Sqrt[3]/(2 Pi)	م	A086089	[0;1,4,1,3,1,1,4,1,2,2,1,1,7,1,4,4,2,1,1,1,1,...]	1939 1949	0.82699334313268807426698974746945416
2.66514414269022518865	ثابتة غيلفوند–شنايدر		$G_{\,GS}$	$2^{\sqrt {2}}$	2^sqrt{2}	م	A007507	[2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...]	1934	2.66514414269022518865029724987313985
3.27582291872181115978	ثابت ليفي		$\gamma$	$e^{\pi ^{2}/(12\ln 2)}$	e^(\pi^2/(12 ln(2))		A086702	[3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...]	1936	3.27582291872181115978768188245384386
0.52382257138986440645	دالة تشي		${\operatorname {Chi()} }$	$\gamma +\int _{0}^{x}{\frac {\cosh t-1}{t}}\,dt$ $\scriptstyle \gamma \,{\text{= 0.5772156649...}}$	Chi(x)		A133746	[0;1,1,9,1,172,1,7,1,11,1,1,2,1,8,1,1,1,1,1,...]		0.52382257138986440645095829438325566
1.1319882487943	ثابت فيسونث		${C}_{Vi}$	$\lim _{n\to \infty }|a_{n}|^{\frac {1}{n}}$      حيثan = عدد فيبوناتشي	lim_(n->∞) |a_n|^(1/n)	م	A078416	[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]	1997	1.1319882487943
1.23370055013616982735	ثابت فاراد		${\tfrac {3}{4}}\zeta (2)$	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots$	sum[n=1 to ∞] {1/((2n-1)^2)}	م	A111003	[1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...]	1902 a 1965	1.23370055013616982735431137498451889
2.50662827463100050241	الجذر التربيعي ل 2 باي		${\sqrt {2\pi }}$	${\sqrt {2\pi }}=\lim _{n\to \infty }{\frac {n!\;e^{n}}{n^{n}{\sqrt {n}}}}{\color {white}....\color {black}}$ تقريب ستيرلينغ	sqrt (2 pi)	م	A019727	[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]	1692 a 1770	2.50662827463100050241576528481104525
4.13273135412249293846	الجذر التربيعي لتاو* مشتقة الدالة الأسية للأساس e		${\sqrt {\tau e}}$	${\sqrt {2\pi e}}$	sqrt(2 pi e)		A019633	[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]		4.13273135412249293846939188429985264
0.97027011439203392574	ثابت لوتش		${{\text{£}}_{_{Lo}}}$	${\frac {6\ln 2\ln 10}{\pi ^{2}}}$	6*ln(2)*ln(10)/Pi^2		A086819	[0;1,32,1,1,1,2,1,46,7,2,7,10,8,1,71,1,37,1,1,...]	1964	0.97027011439203392574025601921001083
0.98770039073605346013	المساحة المحيطة لمثلث رولو		${\mathcal {T}}_{R}$	$a^{2}\cdot \left(2{\sqrt {3}}+{\frac {\pi }{6}}-3\right)$    حيث a= طول ضلع المربع	2 sqrt(3)+pi/6-3	م	A066666	[0;1,80,3,3,2,1,1,1,4,2,2,1,1,1,8,1,2,10,1,2,...]	1914	0.98770039073605346013199991355832854
0.70444220099916559273	ثابت الإهمال 2		${\mathcal {C}}_{2}$	${\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}+1)}}\right)}}$	N[prod[n=1 to ∞] {1 - 1/(prime(n)* (prime(n)+1))}]		A065463	[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...]		0.70444220099916559273660335032663721
1.84775906502257351225	معامل الربط		${\mu }$	${\sqrt {2+{\sqrt {2}}}}\;=\lim _{n\rightarrow \infty }c_{n}^{1/n}$ دالة متعددة الحدود: $\;x^{4}-4x^{2}+2=0$	sqrt(2+sqrt(2))	ج	A179260	[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...]		1.84775906502257351225636637879357657
0.30366300289873265859	ثابت جاووس-كوزمين-يرسينغ		${\lambda }_{2}$	$\lim _{n\to \infty }{\frac {F_{n}(x)-\ln(1-x)}{(-\lambda )^{n}}}=\Psi (x),$ حيث $\Psi (x)$ دالة تحليلية و $\Psi (0)\!=\!\Psi (1)\!=\!0$.			A038517	[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...]	1973	0.30366300289873265859744812190155623
1.57079632679489661923	ثابت فارد K1 جداء واليس		${\frac {\pi }{2}}$	$\prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots$	Prod[n=1 to ∞] {(4n^2)/(4n^2-1)}	م	A069196	[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...]	1655	1.57079632679489661923132169163975144
1.606695152415291763	ثابت إيردوس بروين		${E}_{\,B}$	$\sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {1}{2^{mn}}}=\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!...$	sum[n=1 to ∞] {1/(2^n-1)}	غ.ك	A065442	[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]	1949	1.60669515241529176378330152319092458
1.61803398874989484820	فاي، النسبة الذهبية		${\varphi }$	${\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}$	(1+5^(1/2))/2	ج	A001622	[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...] = [0;1,...]	-300 ~	1.61803398874989484820458683436563811
1.64493406684822643647	دالة ريمان زيتا (2)		${\zeta }(\,2)$	${\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots$	Sum[n=1 to ∞] {1/n^2}	م	A013661	[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]	1826 to 1866	1.64493406684822643647241516664602519
1.73205080756887729352	الجذر التربيعي ل 3		${\sqrt {3}}$	${\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,\cdots }}}}}}}}}}$	(3(3(3(3(3(3(3) ^1/3)^1/3)^1/3) ^1/3)^1/3)^1/3) ^1/3 ...	ج	A002194	[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] = [1;1,2,...]	-465 to -398	1.73205080756887729352744634150587237
1.75793275661800453270	عدد كاسنر		${R}$	${\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}$	Fold[Sqrt[#1+#2] &,0,Reverse [Range[20]]]		A072449	[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]	1878 a 1955	1.75793275661800453270881963821813852
2.29558714939263807403	ثابت القطع المكافئ العالمي		${P}_{\,2}$	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arcsinh} (1)+{\sqrt {2}}$	ln(1+sqrt 2)+sqrt 2	م	A103710	[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...]		2.29558714939263807403429804918949038
1.78657645936592246345	ثابت سيلفرمان		${{\mathcal {S}}_{_{m}}}$	$\sum _{n=1}^{\infty }{\frac {1}{\phi (n)\sigma _{1}(n)}}={\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1+\sum _{k=1}^{\infty }{\frac {1}{p_{n}^{2k}-p_{n}^{k-1}}}\right)}}$ ø() = مؤشر أويلر، σ1() = دالة القواسم.	Sum[n=1 to ∞] {1/[EulerPhi(n) DivisorSigma(1,n)]}		A093827	[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...]		1.78657645936592246345859047554131575
2.59807621135331594029	مساحة شكل سداسي منتظم مع جانب يساوي 1		${\mathcal {A}}_{6}$	${\frac {3{\sqrt {3}}}{2}}$	3 sqrt(3)/2	ج	A104956	[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] [2;1,1,2,20,2,1,1,4]		2.59807621135331594029116951225880855
0.66131704946962233528	ثابت فيلر تورنر		${{\mathcal {C}}_{_{FT}}}$	${\underset {p_{n}:\,{prime}}{{\frac {1}{2}}\prod _{n=1}^{\infty }\left(1-{\frac {2}{p_{n}^{2}}}\right){+}{\frac {1}{2}}}}={\frac {3}{\pi ^{2}}}\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}^{2}-1}}\right){+}{\frac {1}{2}}$	[prod[n=1 to ∞] {1-2/prime(n)^2}] /2 + 1/2	م	A065493	[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...]	1932	0.66131704946962233528976584627411853
1.46099848620631835815	ثابت باكستر	Mapamundi Four-Coloring	${\mathcal {C}}^{2}$	$\prod _{n=1}^{\infty }{\frac {(3n-1)^{2}}{(3n-2)(3n)}}={\frac {3}{4\pi ^{2}}}\,\Gamma \left({\frac {1}{3}}\right)^{3}$ Γ() = دالة غاما	3×Gamma(1/3) ^3/(4 pi^2)		A224273	[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...]	1970	1.46099848620631835815887311784605969
1.92756197548292530426	ثابت تترنك		${\mathcal {T}}$	الجذور الموجبة للمعادلة التالية: $\;\;x^{4}-x^{3}-x^{2}-x-1=0$	Root[x+x^-4-2=0]	ج	A086088	[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...]		1.92756197548292530426190586173662216
1.00743475688427937609	مكعب روبرت الرايني		${f_{(3,4)}}$	الجذور الموجبة للمعادلة التالية: $\;\;4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0$	Root[4*x^8-28*x^6 -7*x^4+16*x^2+16 =0]	ج	A243309	[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...]		1.00743475688427937609825359523109914
1.70521114010536776428	ثابت نيفن		${C}$	$1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)$	1+ Sum[n=2 to ∞] {1-(1/Zeta(n))}		A033150	[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...]	1969	1.70521114010536776428855145343450816
0.6045997880780726168	العلاقة بين مساحة مثلث متساوي الأضلاع والدائر بداخلة		${\frac {\pi }{3{\sqrt {3}}}}$	$\sum _{n=1}^{\infty }{\frac {1}{n{2n \choose n}}}=1-{\frac {1}{2}}+{\frac {1}{4}}-{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{8}}+\cdots$ متسلسلة دركليه	Sum[1/(n Binomial[2 n, n]) , {n, 1, ∞}]	م	A073010	[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...]		0.60459978807807261686469275254738524
1.15470053837925152901	ثابت هيرمت		$\gamma _{_{2}}$	${\frac {2}{\sqrt {3}}}={\frac {1}{\cos \,({\frac {\pi }{6}})}}$	2/sqrt(3)	ج	1+  A246724	[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] [1;6,2]		1.15470053837925152901829756100391491
0.41245403364010759778	ثابت موروس		$\tau$	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}$    حيث $\tau (x)=\sum _{n=0}^{\infty }(-1)^{t_{n}}\,x^{n}=\prod _{n=0}^{\infty }(1-x^{2^{n}})$		م	A014571	[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...]		0.41245403364010759778336136825845528
0.58057755820489240229	ثابت بيل		${{\mathcal {P}}_{_{Pell}}}$	$1-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2n+1}}}\right)$	N[1-prod[n=0 to ∞] {1-1/(2^(2n+1)}]	م	A141848	[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...]		0.58057755820489240229004389229702574
0.66274341934918158097	نهاية لابلاس		${\lambda }$	${\frac {x\;e^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$	(x e^sqrt(x^2+1)) /(sqrt(x^2+1)+1) = 1		A033259	[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...]	1782 ~	0.66274341934918158097474209710925290
0.17150049314153606586	ثابت هال مونتغمري		${{\delta }_{_{0}}}$	$1+{\frac {\pi ^{2}}{6}}+2\;\mathrm {Li} _{2}\left(-{\sqrt {e}}\;\right)\quad \mathrm {Li} _{2}\,\scriptstyle {\text{= Dilogarithm integral}}$	1 + Pi^2/6 + 2*PolyLog[2, -Sqrt[E]]		A143301	[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...]		0.17150049314153606586043997155521210
1.55138752454832039226	مثلث كالبي		${C_{_{CR}}}$	${1 \over 3}+{(-23+3i{\sqrt {237}})^{\tfrac {1}{3}} \over 3\cdot 2^{\tfrac {2}{3}}}+{11 \over 3(2(-23+3i{\sqrt {237}}))^{\tfrac {1}{3}}}$	FindRoot[ 2x^3-2x^2-3x+2 ==0, {x, 1.5}, WorkingPrecision->40]	ج	A046095	[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...]	1946 ~	1.55138752454832039226195251026462381
1.22541670246517764512	غاما(3/4)		$\Gamma ({\tfrac {3}{4}})$	$\left(-1+{\frac {3}{4}}\right)!=\left(-{\frac {1}{4}}\right)!$	(-1+3/4)!		A068465	[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...]		1.22541670246517764512909830336289053
1.20205690315959428539	ثابت أبيري		$\zeta (3)$	$\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots =$ ${\frac {1}{2}}\sum _{n=1}^{\infty }{\frac {H_{n}}{n^{2}}}={\frac {1}{2}}\sum _{i=1}^{\infty }\sum _{j=1}^{\infty }{\frac {1}{ij(i{+}j)}}=\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}{\frac {\mathrm {d} x\mathrm {d} y\mathrm {d} z}{1-xyz}}$	Sum[n=1 to ∞] {1/n^3}	غ.ك	A010774	[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...]	1979	1.20205690315959428539973816151144999
0.91596559417721901505	ثابت كاتالان		${C}$	$\int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {1}{1{+}x^{2}y^{2}}}\,dx\,dy=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }$	Sum[n=0 to ∞] {(-1)^n/(2n+1)^2}	م	A006752	[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...]	1864	0.91596559417721901505460351493238411
0.78539816339744830961	بيتا(1)		${\beta }(1)$	${\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots$	Sum[n=0 to ∞] {(-1)^n/(2n+1)}	م	A003881	[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]	1805 to 1859	0.78539816339744830961566084581987572
0.001317641154853178109	ثابت روجر هيث براون		${C_{_{HBM}}}$	${\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}}}\right)^{7}\left(1+{\frac {7p_{n}+1}{p_{n}^{2}}}\right)}}$	N[prod[n=1 to ∞] {((1-1/prime(n))^7) *(1+(7*prime(n)+1) /(prime(n)^2))}]	م	A118228	[0;758,1,13,1,2,3,56,8,1,1,1,1,1,143,1,1,1,2,...]		0.00131764115485317810981735232251358
0.56755516330695782538	الوحدة النمطية للرفع الوحدة التخيليةi		$|{}^{\infty }{i}|$	$\lim _{n\to \infty }\left|{}^{n}i\right|=\left|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right|$	Mod(i^i^i^...)		A212479	[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]		0.56755516330695782538461314419245334
0.78343051071213440705	حلم الطالب الجامعي (1) ليوهان بيرنولي		${I}_{1}$	$\int _{0}^{1}\!x^{x}\,dx=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}={\frac {1}{1^{1}}}-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\cdots }$	Sum[n=1 to ∞] {-(-1)^n /n^n}		A083648	[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...]	1697	0.78343051071213440705926438652697546
1.291285997062663540407	حلم الطالب الجامعي (2) ليوهان بيرنولي		${I}_{2}$	$\int _{0}^{1}\!{\frac {1}{x^{x}}}\,dx=\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}={\frac {1}{1^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+\cdots$	Sum[n=1 to ∞] {1/(n^n)}		A073009	[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...]	1697	1.29128599706266354040728259059560054
0.70523017179180096514	ثابت بريموريال		${P_{\#}}$	${\underset {p_{n}:\,{prime}}{\sum _{n=1}^{\infty }{\frac {1}{p_{n}\#}}={\frac {1}{2}}+{\frac {1}{6}}+{\frac {1}{30}}+{\frac {1}{210}}+...=\sum _{k=1}^{\infty }\prod _{n=1}^{k}{\frac {1}{p_{n}}}}}$	Sum[k=1 to ∞] (prod[n=1 to k] {1/prime(n)})	غ.ك	A064648	[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...]		0.70523017179180096514743168288824851
0.14758361765043327417	صيغة بيلي-بوروين-بلوف		${C}$	${\frac {1}{\pi }}\arctan {\frac {1}{2}}={\frac {1}{\pi }}\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2^{2n+1})(2n+1)}}$ $={\frac {1}{\pi }}\left({\frac {1}{2}}-{\frac {1}{3\cdot 2^{3}}}+{\frac {1}{5\cdot 2^{5}}}-{\frac {1}{7\cdot 2^{7}}}+\cdots \right)$	Arctan(1/2)/pi	م	A086203	[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...]		0.14758361765043327417540107622474052
0.15915494309189533576	ثابت بلوف		${A}$	${\frac {1}{2\pi }}$	1/(2 pi)	م	A086201	[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...]		0.15915494309189533576888376337251436
0.29156090403081878013	ثابت ديمر ثنائي الأبعاد 2D,		${\frac {C}{\pi }}$ C= ثابت كاتالان	$\int \limits _{-\pi }^{\pi }{\frac {\cosh ^{-1}\left({\frac {\sqrt {\cos(t)+3}}{\sqrt {2}}}\right)}{4\pi }}\,dt$	N[int[-pi to pi] {arccosh(sqrt( cos(t)+3)/sqrt(2)) /(4*Pi)dt}]		A143233	[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]		0.29156090403081878013838445646839491
0.498015668118356042 0.15494982830181068512 i	المضروب (i)		${i}\,!$	$\Gamma (1+i)=i\,\Gamma (i)=\int \limits _{0}^{\infty }{\frac {t^{i}}{e^{t}}}\mathrm {d} t$	Integral_0^∞ t^i/e^t dt	خ	A212877  A212878	[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i		0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i
2.09455148154232659148	ثابت واليس		$W$	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}$	(((45-sqrt(1929)) /18))^(1/3)+ (((45+sqrt(1929)) /18))^(1/3)	ج	A007493	[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...]	1616 to 1703	2.09455148154232659148238654057930296
0.723648402298200009408	ثابت سرناك		${C_{sa}}$	$\prod _{p>2}{\Big (}1-{\frac {p+2}{p^{3}}}{\Big )}$	N[prod[k=2 to ∞] {1-(prime(k)+2) /(prime(k)^3)}]	م	A065476	[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...]		0.72364840229820000940884914980912759
0.632120558828557678404	الثابت الزمني		${\tau }$	$\lim _{n\to \infty }1-{\frac {!n}{n!}}=\lim _{n\to \infty }P(n)=\int _{0}^{1}e^{-x}dx=1{-}{\frac {1}{e}}=$ $\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n!}}={\frac {1}{1!}}{-}{\frac {1}{2!}}{+}{\frac {1}{3!}}{-}{\frac {1}{4!}}{+}{\frac {1}{5!}}{-}{\frac {1}{6!}}{+}\cdots$	lim_(n->∞) (1- !n/n!) !n=subfactorial	م	A068996	[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;1,1,1,2n], n∈ℕ		0.63212055882855767840447622983853913
1.04633506677050318098	ثابت مينكوفسكي-سيجل		$F_{1}$	$\prod _{n=1}^{\infty }{\frac {n!}{{\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}{\sqrt[{12}]{1+{\tfrac {1}{n}}}}}}$	N[prod[n=1 to ∞] n! /(sqrt(2*Pi*n) *(n/e)^n *(1+1/n) ^(1/12))]		A213080	[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..]	1867 1885 1935	1.04633506677050318098095065697776037
5.244115108584239620929	ثابت ليمنيسكيت		$2\varpi$	${\frac {[\Gamma ({\tfrac {1}{4}})]^{2}}{\sqrt {2\pi }}}=4\int _{0}^{1}{\frac {dx}{\sqrt {(1-x^{2})(2-x^{2})}}}$	Gamma[ 1/4 ]^2 /Sqrt[ 2 Pi ]		A064853	[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...]	1718	5.24411510858423962092967917978223883
0.661707182267176235155	ثابت روبين		$\Delta (3)$	${\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}$	(4+17*2^(1/2)-6 *3^(1/2)+21*ln(1+ 2^(1/2))+42*ln(2+ 3^(1/2))-7*Pi)/105		A073012	[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...]	1978	0.66170718226717623515583113324841358
1.30357726903429639125	ثابت كونواي		${\lambda }$	${\begin{smallmatrix}x^{71}\quad \ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad \ -7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}\quad \ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}$		ج	A014715	[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...]	1987	1.30357726903429639125709911215255189
1.18656911041562545282	ثابت ليفي		${\beta }$	${\frac {\pi ^{2}}{12\,\ln 2}}$	pi^2 /(12 ln 2)		A100199	[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...]	1935	1.18656911041562545282172297594723712
0.83564884826472105333	مبرهنة باكر		$\beta _{3}$	$\int _{0}^{1}{\frac {\mathrm {d} t}{1+t^{3}}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{3n+1}}={\frac {1}{3}}\left(\ln 2+{\frac {\pi }{\sqrt {3}}}\right)$	Sum[n=0 to ∞] {((-1)^(n))/(3n+1)}		A113476	[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...]		0.83564884826472105333710345970011076
23.10344790942054161603	متتالية كيمبنر(0)		${K_{0}}$	$1{+}{\frac {1}{2}}{+}{\frac {1}{3}}{+}\cdots {+}{\frac {1}{9}}{+}{\frac {1}{11}}{+}\cdots {+}{\frac {1}{19}}{+}{\frac {1}{21}}{+}\cdots$ ${+}{\frac {1}{99}}{+}{\frac {1}{111}}{+}\cdots {+}{\frac {1}{119}}{+}{\frac {1}{121}}{+}\cdots$	1+1/2+1/3+1/4+1/5 +1/6+1/7+1/8+1/9 +1/11+1/12+1/13 +1/14+1/15+...		A082839	[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...]		23.1034479094205416160340540433255981
0.989431273831146951741	ثابت ليبسج		${C_{1}}$	$\lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)$	4/pi^2*[(2 Sum[k=1 to ∞] {ln(k)/(4*k^2-1)}) -poligamma(1/2)]		A243277	[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...]		0.98943127383114695174164880901886671
0.19452804946532511361	المعامل الثاني لدي بو ريموند		${C_{2}}$	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right|\,dt-1$	(e^2-7)/2	م	A062546	[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...] = [0;2p+3], p∈ℕ		0.19452804946532511361521373028750390
0.78853056591150896106	ثابت لورث		$C_{L}$	$\sum _{n=2}^{\infty }{\frac {\ln \left({\frac {n}{n-1}}\right)}{n}}$	Sum[n=2 to ∞] log(n/(n-1))/n		A085361	[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...]		0.78853056591150896106027632216944432
1.187452351126501054595	ثابت غوياس α		$F_{\alpha }$	$x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots$			A085848	[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...]	2000	1.18745235112650105459548015839651935
2.293166287411861031508	ثابت غوياس β		$F_{\beta }$	$x^{x+1}=(x+1)^{x}$	x^(x+1) = (x+1)^x		A085846	[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...]	2000	2.29316628741186103150802829125080586
0.82246703342411321823	ثابت نيسلون-رامانجن		${\frac {{\zeta }(2)}{2}}$	${\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}{-}\cdots$	Sum[n=1 to ∞] {((-1)^(n+1))/n^2}	م	A072691	[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...]	1909	0.82246703342411321823620758332301259
0.69314718055994530941	اللوغارتم الطبيعي للرقم 2		$Ln(2)$	$\sum _{n=1}^{\infty }{\frac {1}{n2^{n}}}=\sum _{n=1}^{\infty }{\frac {({-}1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\cdots }$	Sum[n=1 to ∞] {(-1)^(n+1)/n}	م	A002162	[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...]	1550 to 1617	0.69314718055994530941723212145817657
0.47494937998792065033	ثابت ويرستراس		$\sigma ({\tfrac {1}{2}})$	${\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{4\cdot 2^{3/4}{({\frac {1}{4}}!)^{2}}}}$	(E^(Pi/8) Sqrt[Pi]) /(4 2^(3/4) (1/4)!^2)		A094692	[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...]	1872	0.47494937998792065033250463632798297
0.577215664901532860606	ثابت أويلر-ماسكيروني		${\gamma }$	$\sum _{n=1}^{\infty }\sum _{k=0}^{\infty }{\frac {(-1)^{k}}{2^{n}+k}}=\sum _{n=1}^{\infty }\left({\frac {1}{n}}-\ln \left(1+{\frac {1}{n}}\right)\right)$ $=\int _{0}^{1}-\ln \left(\ln {\frac {1}{x}}\right)\,dx=-\Gamma '(1)=-\Psi (1)$	sum[n=1 to ∞] |sum[k=0 to ∞] {((-1)^k)/(2^n+k)}		A001620	[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,...]	1735	0.57721566490153286060651209008240243
1.38135644451849779337	ثابت بيتا كينسر ماهلر لمتعددة الحدود		$\beta$	$e^{^{\textstyle {\frac {2}{\pi }}\displaystyle {\int _{0}^{\frac {\pi }{3}}}\textstyle {t\tan t\ dt}}}=e^{^{\displaystyle {\,\int _{\frac {-1}{3}}^{\frac {1}{3}}}\textstyle {\,\ln \lfloor 1+e^{2\pi it}}\rfloor dt}}$	e^((PolyGamma(1,4/3) - PolyGamma(1,2/3) +9)/(4*sqrt(3)*Pi))		A242710	[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...]	1963	1.38135644451849779337146695685062412
1.358456274182988435206	الدوامة الذهبية		$c$	$\varphi ^{\frac {2}{\pi }}=\left({\frac {1+{\sqrt {5}}}{2}}\right)^{\frac {2}{\pi }}$	GoldenRatio^(2/pi)		A212224	[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...]		1.35845627418298843520618060050187945
0.57595996889294543964	ثابت ستيفين		$C_{S}$	$\prod _{n=1}^{\infty }\left(1-{\frac {p}{p^{3}-1}}\right)$	Prod[n=1 to ∞] {1-hprime(n) /(hprime(n)^3-1)}	م	A065478	[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...]		0.57595996889294543964316337549249669
0.73908513321516064165	عدد دوتي		$d$	$\lim _{x\to \infty }\cos ^{[x]}(c)=\lim _{x\to \infty }\underbrace {\cos(\cos(\cos(\cdots (\cos(c)))))} _{x}$	cos(c)=c	م	A003957	[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...]		0.73908513321516064165531208767387340
0.67823449191739197803	ثابت تانيجوتشي		$C_{T}$	خطأ رياضيات (خطأ في الصياغة): {\displaystyle \prod_{n = 1}^\infty \left(1 - \frac{3}{{p_n}^3}+\frac{2}{{p_n}^4}+rac{1}{{p_n}^5}-rac{1}{{p_n}^6} ight) } $\scriptstyle p_{n}=\,ext{prime}$	Prod[n=1 to ∞] {1 -3/ithprime(n)^3 +2/ithprime(n)^4 +1/ithprime(n)^5 -1/ithprime(n)^6}	م	A175639	[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...]		0.67823449191739197803553827948289481
1.85407467730137191843	ثابت جاووس ليمنيسكيت		$L{\text{/}}{\sqrt {2}}$	$\int \limits _{0}^{\infty }{\frac {\mathrm {d} x}{\sqrt {1+x^{4}}}}={\frac {1}{4{\sqrt {\pi }}}}\,\Gamma \left({\frac {1}{4}}\right)^{2}={\frac {4\left({\frac {1}{4}}!\right)^{2}}{\sqrt {\pi }}}$ $\scriptstyle \Gamma (){\text{= Gamma function}}$	pi^(3/2)/(2 Gamma(3/4)^2)		A093341	[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...]		1.85407467730137191843385034719526005
1.75874362795118482469	ثابت الضرب اللانهائي		$Pr_{1}$	$\prod _{n=2}^{\infty }{\Big (}1+{\frac {1}{n}}{\Big )}^{\frac {1}{n}}$	Prod[n=2 to inf] {(1+1/n)^(1/n)}		A242623	[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...]	1977	1.75874362795118482469989684865589317
1.86002507922119030718	حلزون تيودوروس		$\partial$	$\sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n^{3}}}+{\sqrt {n}}}}=\sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n}}(n+1)}}$	Sum[n=1 to ∞] {1/(n^(3/2) +n^(1/2))}		A226317	[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...]	-460 to -399	1.86002507922119030718069591571714332
2.79128 78474 77920 00329	متداخلة جذرية S5		$S_{5}$	$\displaystyle {\frac {{\sqrt {21}}+1}{2}}=\scriptstyle \,{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5+\cdots }}}}}}}}}}\;$ $=1+\,\scriptstyle {\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-\cdots }}}}}}}}}}\;$	(sqrt(21)+1)/2	ج	A222134	[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...] [2;1,3]		2.79128784747792000329402359686400424
0.70710678118654752 br> +0.70710 67811 86547 524 i>	الجذر التربيعي للوحدة التخيليةi		${\sqrt {i}}$	${\sqrt[{4}]{-1}}={\frac {1+i}{\sqrt {2}}}=e^{\frac {i\pi }{4}}=\cos \left({\frac {\pi }{4}}\right)+i\sin \left({\frac {\pi }{4}}\right)$	(1+i)/(sqrt 2)	ج خ	A010503	[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] = [0;1,2,...] [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i = [0;1,2,...] i		0.70710678118654752440084436210484903 + 0.70710678118654752440084436210484 i
0.809394020540639130717	ثابت اللادي – جرينستيد		${{\mathcal {A}}_{AG}}$	$e^{-1+\sum \limits _{k=2}^{\infty }\sum \limits _{n=1}^{\infty }{\frac {1}{nk^{n+1}}}}=e^{-1-\sum \limits _{k=2}^{\infty }{\frac {1}{k}}\ln \left(1-{\frac {1}{k}}\right)}$	e^{(sum[k=2 to ∞] |sum[n=1 to ∞] {1/(n k^(n+1))})-1}		A085291	[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...]	1977	0.80939402054063913071793188059409131
2.58498175957925321706	ثابت شيربينسكي		${K}$	$\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )$ $=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)$	-Pi Log[Pi]+2 Pi EulerGamma +4 Pi Log [Gamma[3/4]]		A062089	[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...]	1907	2.58498175957925321706589358738317116
1.73245471460063347358	ثابت أويلر – ماتشيروني		${\frac {1}{\gamma }}$	$\left(\int _{0}^{1}-\log \left(\log {\frac {1}{x}}\right)\,dx\right)^{-1}=\sum _{n=1}^{\infty }(-1)^{n}(-1+\gamma )^{n}$	1/Integrate_ {x=0 to 1} -log(log(1/x))		A098907	[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]		1.73245471460063347358302531586082968
1.435991124176917432355	ثابت يبيسج		${L_{1}}$	$\prod _{\begin{smallmatrix}i=0\\j\neq i\end{smallmatrix}}^{n}{\frac {x-x_{i}}{x_{j}-x_{i}}}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\lfloor \sin {\frac {3t}{2}}\rfloor }{\sin {\frac {t}{2}}}}\,dt={\frac {1}{3}}+{\frac {2{\sqrt {3}}}{\pi }}$	1/3 + 2*sqrt(3)/pi	م	A226654	[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...]	1902 ~	1.43599112417691743235598632995927221
3.24697960371746706105	الجذر الفضي		$\varsigma$	$2+2\cos {\frac {2\pi }{7}}=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}$	2+2 cos(2Pi/7)	ج	A116425	[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]		3.24697960371746706105000976800847962
1.94359643682075920505	مؤشر أويلر		$ET$	${\underset {p{\text{= primes}}}{\prod _{p}{\Big (}1+{\frac {1}{p(p-1)}}{\Big )}}}={\frac {\zeta (2)\zeta (3)}{\zeta (6)}}={\frac {315\zeta (3)}{2\pi ^{4}}}$	zeta(2)*zeta(3) /zeta(6)		A082695	[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...]	1750	1.94359643682075920505707036257476343
1.495348781221220541911	الجذر الرابع ل5		${\sqrt[{4}]{5}}$	${\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,\cdots }}}}}}}}}}$	(5(5(5(5(5(5(5) ^1/5)^1/5)^1/5) ^1/5)^1/5)^1/5) ^1/5 ...	ج	A011003	[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...]		1.49534878122122054191189899414091339
0.87228404106562797617	مساحة دائرة فورد		$A_{CF}$	$\sum _{q\geq 1}\sum _{(p,q)=1 \atop 1\leq p<q}\pi \left({\frac {1}{2q^{2}}}\right)^{2}{\underset {\zeta (){\text{= Riemann Zeta Function}}}{={\frac {\pi }{4}}{\frac {\zeta (3)}{\zeta (4)}}={\frac {45}{2}}{\frac {\zeta (3)}{\pi ^{3}}}}}$	pi Zeta(3) /(4 Zeta(4))			[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...]		0.87228404106562797617519753217122587
1.08232323371113819151	زيتا(4)		$\zeta (4)$	${\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+...$	Sum[n=1 to ∞] {1/n^4}	م	A013662	[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...]	?	1.08232323371113819151600369654116790
1.56155281280883027491	عدد مثلثي مربعي للرقم 2.		${R_{2}}$	${\frac {{\sqrt {17}}-1}{2}}=\,\scriptstyle {\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+{\sqrt {4+\cdots }}}}}}}}}}}}\,\,-1$ $=\,\scriptstyle {\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-\cdots }}}}}}}}}}}}\textstyle$	(sqrt(17)-1)/2	ج	A222133	[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] [1;1,1,3]		1.56155281280883027491070492798703851
9.86960440108935861883	مربع باي		${\pi }^{2}$	$6\,\zeta (2)=6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots$	6 Sum[n=1 to ∞] {1/n^2}	م	A002388	[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...]		9.86960440108935861883449099987615114
1.32471795724474602596	العدد البلاستيكي		${\rho }$	${\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+\!{\sqrt {\frac {23}{108}}}}}+\!{\sqrt[{3}]{{\frac {1}{2}}-\!{\sqrt {\frac {23}{108}}}}}$	(1+(1+(1+(1+(1+(1) ^(1/3))^(1/3))^(1/3)) ^(1/3))^(1/3))^(1/3)	ج	A060006	[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...]	1929	1.32471795724474602596090885447809734
2.37313822083125090564	ثابت ليفي2		$2\,ln\,\gamma$	${\frac {\pi ^{2}}{6ln(2)}}$	Pi^(2)/(6*ln(2))	م	A174606	[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]	1936	2.37313822083125090564344595189447424
0.85073618820186726036	متسلسلة طوي الورق		${P_{f}}$	$\sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}$	N[Sum[n=0 to ∞] {8^2^n/(2^2^ (n+2)-1)},37]		A143347	[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...]		0.85073618820186726036779776053206660
1.1563626843322697168533	ثابت تكرار المكعب		${\sigma _{3}}$	$\prod _{n=1}^{\infty }n^{{3}^{-n}}={\sqrt[{3}]{1{\sqrt[{3}]{2{\sqrt[{3}]{3\cdots }}}}}}=1^{1/3}\;2^{1/9}\;3^{1/27}\cdots$	prod[n=1 to ∞] {n ^(1/3)^n}		A123852	[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...]		1.15636268433226971685337032288736935
1.261859507142914874199	البعد الكسري لمنحنى ندفة الثلج لكوخ		${C_{k}}$	${\frac {\log 4}{\log 3}}$	log(4)/log(3)	م	A100831	[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...]		1.26185950714291487419905422868552171
6.58088599101792097085	ثابت فورودا		$2^{\,e}$	$2^{e}$	2^e			[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]		6.58088599101792097085154240388648649
0.26149 72128 47642 78375	ثابت ميرتنز-ميسيل		${M}$	$\lim _{n\rightarrow \infty }\!\!\left(\sum _{p\leq n}{\frac {1}{p}}\!-\ln(\ln(n))\!\right)\!\!={\underset {\!\!\!\!\gamma :\,{\text{Euler constant}},\,\,p:\,{\text{prime}}}{\!\gamma \!+\!\!\sum _{p}\!\left(\!\ln \!\left(\!1\!-\!{\frac {1}{p}}\!\right)\!\!+\!{\frac {1}{p}}\!\right)}}$	gamma+ Sum[n=1 to ∞] {ln(1-1/prime(n)) +1/prime(n)}	م	A077761	[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...]	1866 & 1873	0.26149721284764278375542683860869585
4.81047738096535165547	ثابت جون		$\gamma$	${\sqrt[{i}]{i}}=i^{-i}=(i^{i})^{-1}=(((i)^{i})^{i})^{i}=e^{\frac {\pi }{2}}={\sqrt {\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}}}$	e^(π/2)	م	A042972	[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...]		4.81047738096535165547303566670383313
- 0.5 ± 0.86602540378443 i	الجذر التكعيبي للرقم 1