قائمة الثوابت الرياضية
جدول الدوال والثوابت الرياضية

| 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  |