গাণিতিক ধ্ৰুৱকৰ তালিকা

গাণিতিক ধ্ৰুৱক (ইংৰাজী: Mathematical constants) হৈছে এনে এটা সংখ্যা যাৰ মান এটা দ্ব্যৰ্থহীন সংজ্ঞাৰ দ্বাৰা নিৰ্ধাৰণ কৰা হয়। ইয়াক প্ৰায়ে এটা চিহ্ন (যেনে, বৰ্ণমালাৰ আখৰ) বা গণিতজ্ঞসকলৰ নামেৰে উল্লেখ কৰা হয়। উদাহৰণস্বৰূপে, ধ্ৰুৱক π (পাই) ক এটা বৃত্তৰ পৰিধিৰ দৈৰ্ঘ্য আৰু ইয়াৰ ব্যাসৰ অনুপাত হিচাপে সংজ্ঞায়িত কৰিব পাৰি।

তালিকা

নাম	চিহ্ন	দশমিক প্ৰসাৰণ	সূত্ৰ	বৰ্ষ	সংহতি
এক	১	১		প্ৰাক‌ঐতিহাসিক	$\mathbb {N}$
দুই	২	২		প্ৰাক‌ঐতিহাসিক	$\mathbb {N}$
আধা	১/২	০.৫		প্ৰাক‌ঐতিহাসিক	$\mathbb {Q}$
পাই	$\pi$	৩.১৪১৫৯ ২৬৫৩৫ ৮৯৭৯৩	এটা বৃত্তৰ পৰিধি আৰু ব্যাসৰ অনুপাত।	খ্ৰীষ্টাব্দ ১৯০০ – ১৬০০	$\mathbb {R} \setminus \mathbb {A}$
টাউ (গাণিতিক ধ্ৰুৱক)	$\tau$	৬.২৮৩১৮ ৫৩০৭১ ৭৯৫৮৬ ৪৭৬৯২	এটা বৃত্তৰ পৰিধি আৰু ইয়াৰ ব্যাসাৰ্ধৰ অনুপাত। $2\pi$ ৰ সমতুল্য।	খ্ৰীষ্টাব্দ ১৯০০ – ১৬০০	$\mathbb {R} \setminus \mathbb {A}$
দুইৰ বৰ্গমূল, পাইথাগোৰাছৰ ধ্ৰুৱক	${\sqrt {2}}$	১.৪১৪২১ ৩৫৬২৩ ৭৩০৯৫ ০৪৮৮০	$x^{2}=2$ ৰ ধনাত্মক মূল।	খ্ৰীষ্টাব্দ ১৮০০ – ১৬০০	$\mathbb {A}$
৩ ৰ বৰ্গমূল, থিঅ'ডৰাছৰ ধ্ৰুৱক	${\sqrt {3}}$	১.৭৩২০৫ ০৮০৭৫ ৬৮৮৭৭ ২৯৩৫২	$x^{2}=3$ ৰ ধনাত্মক মূল।	খ্ৰীষ্টাব্দ ৪৬৫ – ৩৯৮	$\mathbb {A}$
৫ ৰ বৰ্গমূল	${\sqrt {5}}$	২.২৩৬০৬ ৭৯৭৭৪ ৯৯৭৮৯ ৬৯৬৪০	$x^{2}=5$ ৰ ধনাত্মক মূল।		$\mathbb {A}$
ফাই, সোণালী অনুপাত	$\varphi$ বা $\phi$	১.৬১৮০৩ ৩৯৮৮৭ ৪৯৮৯৪ ৮৪৮২০	${\frac {1+{\sqrt {5}}}{2}}$	খ্ৰীষ্টাব্দ ~৩০০	$\mathbb {A}$
ৰূপালী অনুপাত	$\delta _{S}$	২.৪১৪২১ ৩৫৬২৩ ৭৩০৯৫ ০৪৮৮০	${\sqrt {2}}+1$	খ্ৰীষ্টাব্দ ~৩০০	$\mathbb {A}$
শূণ্য	০	০		খ্ৰীষ্টাব্দ ৩০০ – ১০০	$\mathbb {Z}$
ঋণাত্মক এক	−১	−১		খ্ৰীষ্টাব্দ ৩০০ – ২০০	$\mathbb {Z}$
২ ৰ ঘনমূল	${\sqrt[{3}]{2}}$	১.২৫৯৯২ ১০৪৯৮ ৯৪৮৭৩ ১৬৪৭৬	$x^{3}=2$ ৰ প্ৰকৃত মূল।	৪৬ – ১২০ খ্ৰীষ্টাব্দ	$\mathbb {A}$
৩ ৰ ঘনমূল	${\sqrt[{3}]{3}}$	১.৪৪২২৪ ৯৫৭০৩ ০৭৪০৮ ৩৮২৩২	$x^{3}=3$ ৰ প্ৰকৃত মূল।		$\mathbb {A}$
Twelfth root of 2	${\sqrt[{12}]{2}}$	1.05946 30943 59295 26456	$x^{12}=2$ ৰ প্ৰকৃত মূল।		$\mathbb {A}$
Supergolden ratio	$\psi$	1.46557 12318 76768 02665	${\frac {1+{\sqrt[{3}]{\frac {29+3{\sqrt {93}}}{2}}}+{\sqrt[{3}]{\frac {29-3{\sqrt {93}}}{2}}}}{3}}$ $x^{3}=x^{2}+1$ ৰ প্ৰকৃত মূল।		$\mathbb {A}$
কাল্পনিক একক	$i$	0 + 1i	Either of the two roots of $x^{2}=-1$	১৫০১ – ১৫৭৬	$\mathbb {C}$
হেক্সাগনেল লেটিচৰ বাবে সংযোগী ধ্ৰুৱক	$\mu$	1.84775 90650 22573 51225	${\sqrt {2+{\sqrt {2}}}}$, as a root of the polynomial $x^{4}-4x^{2}+2=0$	১৫৯৩	$\mathbb {A}$
কেপলাৰ-বাউকেম্প ধ্ৰুৱক	$K'$	0.11494 20448 53296 20070	$\prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...$	১৫৯৬
ৱালিছৰ ধ্ৰুৱক		2.09455 14815 42326 59148	${\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}$ Real root of $x^{3}-2x-5=0$	১৬১৬ – ১৭০৩	$\mathbb {A}$
অয়লাৰৰ সংখ্যা	$e$	২.৭১৮২৮ ১৮২৮৪ ৫৯০৪৫ ২৩৫৩৬	$\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}=\sum _{n=0}^{\infty }{\frac {1}{n!}}=1+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}\cdots$	১৬১৮	$\mathbb {R} \setminus \mathbb {A}$
২ ৰ স্বাভাৱিক ঘাতাংক	$\ln 2$	0.69314 71805 59945 30941	$e^{x}=2$ ৰ প্ৰকৃত মূল $\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+\cdots$	১৬১৯ আৰু ১৬৬৮	$\mathbb {R} \setminus \mathbb {A}$
Lemniscate constant	$\varpi$	2.62205 75542 92119 81046	$\pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}$ where $G$ is Gauss's constant	১৭১৮ – ১৭৯৮	$\mathbb {R} \setminus \mathbb {A}$
অয়লাৰৰ ধ্ৰুৱক	$\gamma$	0.57721 56649 01532 86060	$\lim _{n\to \infty }\left(-\log n+\sum _{k=1}^{n}{\frac {1}{k}}\right)=\int _{1}^{\infty }\left(-{\frac {1}{x}}+{\frac {1}{\lfloor x\rfloor }}\right)\,dx$	১৭৩৫
Erdős–Borwein constant	$E$	1.60669 51524 15291 76378	$\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!\cdots$	১৭৪৯	$\mathbb {R} \setminus \mathbb {Q}$
অ'মেগা ধ্ৰুৱক	$\Omega$	0.56714 32904 09783 87299	$W(1)={\frac {1}{\pi }}\int _{0}^{\pi }\log \left(1+{\frac {\sin t}{t}}e^{t\cot t}\right)dt$ where W is the Lambert W function	১৭৫৮ আৰু ১৭৮৩	$\mathbb {R} \setminus \mathbb {A}$
Apéry's constant	$\zeta (3)$	1.20205 69031 59594 28539	$\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}={\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{3}}}+{\frac {1}{5^{3}}}+\cdots$	১৭৮০	$\mathbb {R} \setminus \mathbb {Q}$
লাপলাছ সীমা		0.66274 34193 49181 58097	Real root of ${\frac {xe^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1$	~১৭৮২	$\mathbb {R} \setminus \mathbb {A}$
Ramanujan–Soldner constant	$\mu$	1.45136 92348 83381 05028	$\mathrm {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}=0$; root of the logarithmic integral function.	১৭৯২
গাউছৰ ধ্ৰুৱক	$G$	0.83462 68416 74073 18628	${\frac {1}{\mathrm {agm} (1,{\sqrt {2}})}}={\frac {\Gamma ({\frac {1}{4}})^{2}}{2{\sqrt {2\pi ^{3}}}}}={\frac {2}{\pi }}\int _{0}^{1}{\frac {dx}{\sqrt {1-x^{4}}}}$ where agm is the arithmetic–geometric mean	১৭৯৯	$\mathbb {R} \setminus \mathbb {A}$
দ্বিতীয় হাৰমাইট ধ্ৰুৱক	$\gamma _{2}$	1.15470 05383 79251 52901	${\frac {2}{\sqrt {3}}}$	১৮২২ – ১৯০১	$\mathbb {A}$
Liouville's constant	$L$	0.11000 10000 00000 00000 0001	$\sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots$	১৮৪৪ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
First continued fraction constant	$C_{1}$	0.69777 46579 64007 98201	${\tfrac {1}{1+{\tfrac {1}{2+{\tfrac {1}{3+{\tfrac {1}{4+{\tfrac {1}{5+\cdots }}}}}}}}}}$ ${\frac {I_{1}(2)}{I_{0}(2)}}$, where $I_{\alpha }(x)$ is the modified Bessel function	১৮৫৫	$\mathbb {R} \setminus \mathbb {Q}$
ৰামানুজনৰ ধ্ৰুৱক		262 53741 26407 68743 .99999 99999 99250 073	$e^{\pi {\sqrt {163}}}$	১৮৫৯	$\mathbb {R} \setminus \mathbb {A}$
Glaisher–Kinkelin constant	$A$	1.28242 71291 00622 63687	$e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}$	১৮৬০
Catalan's constant	$G$	0.91596 55941 77219 01505	$\int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {dx\,dy}{1{+}x^{2}y^{2}}}=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }$	১৮৬৪
Dottie number		0.73908 51332 15160 64165	Real root of $\cos x=x$	১৮৬৫	$\mathbb {R} \setminus \mathbb {A}$
Meissel–Mertens constant	$M$	0.26149 72128 47642 78375	$\lim _{n\to \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln \ln n\right)=\gamma +\sum _{p}\left(\ln \left(1-{\frac {1}{p}}\right)+{\frac {1}{p}}\right)$ where γ is the Euler–Mascheroni constant and p is prime	১৮৬৬ আৰু ১৮৭৩
Universal parabolic constant	$P$	2.29558 71493 92638 07403	$\ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arsinh} (1)+{\sqrt {2}}$	১৮৯১ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
Cahen's constant	$C$	0.64341 05462 88338 02618	$\sum _{k=1}^{\infty }{\frac {(-1)^{k}}{s_{k}-1}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{6}}-{\frac {1}{42}}+{\frac {1}{1806}}{\,\pm \cdots }$ where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...	১৮৯১	$\mathbb {R} \setminus \mathbb {A}$
Gelfond's constant	$e^{\pi }$	23.14069 26327 79269 0057	$(-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}=1+{\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2}}+{\frac {\pi ^{3}}{6}}+\cdots$	১৯০০	$\mathbb {R} \setminus \mathbb {A}$
Gelfond–Schneider constant	$2^{\sqrt {2}}$	2.66514 41426 90225 18865		১৯০২ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
Second Favard constant	$K_{2}$	1.23370 05501 36169 82735	${\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots$	১৯০২ – ১৯৬৫	$\mathbb {R} \setminus \mathbb {A}$
সোণালী কোণ	$g$	2.39996 32297 28653 32223	${\frac {2\pi }{\varphi ^{2}}}=\pi (3-{\sqrt {5}})$ or $180(3-{\sqrt {5}})=137.50776\ldots$ in degrees	১৯০৭	$\mathbb {R} \setminus \mathbb {A}$
Sierpiński's constant	$K$	2.58498 17595 79253 21706	${\begin{aligned}&\pi \left(2\gamma +\ln {\frac {4\pi ^{3}}{\Gamma ({\tfrac {1}{4}})^{4}}}\right)=\pi (2\gamma +4\ln \Gamma ({\tfrac {3}{4}})-\ln \pi )\\&=\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)\end{aligned}}$	১৯০৭
লেণ্ডাউ-ৰামানুজন ধ্ৰুৱক	$K$	0.76422 36535 89220 66299	${\frac {1}{\sqrt {2}}}\prod _{{p\equiv 3{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}\!\!={\frac {\pi }{4}}\prod _{{p\equiv 1{\text{ mod }}4} \atop p\;{\rm {prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}$	১৯০৮
First Nielsen–Ramanujan constant	$a_{1}$	0.82246 70334 24113 21823	${\frac {{\zeta }(2)}{2}}={\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}\cdots$	১৯০৯	$\mathbb {R} \setminus \mathbb {A}$
Gieseking constant	$G$	1.01494 16064 09653 62502	${\frac {3{\sqrt {3}}}{4}}\left(1-\sum _{n=0}^{\infty }{\frac {1}{(3n+2)^{2}}}+\sum _{n=1}^{\infty }{\frac {1}{(3n+1)^{2}}}\right)=$ $\textstyle {\frac {3{\sqrt {3}}}{4}}\left(1-{\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}-{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}-{\frac {1}{8^{2}}}+{\frac {1}{10^{2}}}\pm \cdots \right)$.	১৯১২
বাৰ্ণষ্টাইনৰ ধ্ৰুৱক	$\beta$	0.28016 94990 23869 13303	$\lim _{n\to \infty }2nE_{2n}(f)$, where En(f) is the error of the best uniform approximation to a real function f(x) on the interval [−1, 1] by real polynomials of no more than degree n, and f(x) = |x|	১৯১৩
ট্ৰিব'নাকি ধ্ৰুৱক		1.83928 67552 14161 13255	${\textstyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {33}}}}+{\sqrt[{3}]{19-3{\sqrt {33}}}}}{3}}={\frac {1+4\cosh \left({\frac {1}{3}}\cosh ^{-1}\left(2+{\frac {3}{8}}\right)\right)}{3}}}$ Real root of $x^{3}-x^{2}-x-1=0$	১৯১৪ – ১৯৬৩	$\mathbb {A}$
Brun's constant	$B_{2}$	1.90216 05831 04	$\textstyle {\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+2}})}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots$ where the sum ranges over all primes p such that p + 2 is also a prime	১৯১৯
Twin primes constant	$C_{2}$	0.66016 18158 46869 57392	$\prod _{\textstyle {p\;{\rm {prime}} \atop p\geq 3}}\left(1-{\frac {1}{(p-1)^{2}}}\right)$	১৯২২
প্লাষ্টিক অনুপাত	$\rho$	1.32471 79572 44746 02596	${\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {\sqrt {69}}{18}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {\sqrt {69}}{18}}}}$ Real root of $x^{3}=x+1$	১৯২৪	$\mathbb {A}$
Bloch's constant	$B$	$0.4332\leq B\leq 0.4719$	The best known bounds are ${\frac {\sqrt {3}}{4}}+2\times 10^{-4}\leq B\leq {\sqrt {\frac {{\sqrt {3}}-1}{2}}}\cdot {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {11}{12}})}{\Gamma ({\frac {1}{4}})}}$	১৯২৫
Z score for the 97.5 percentile point	$z_{.975}$	1.95996 39845 40054 23552	${\sqrt {2}}\operatorname {erf} ^{-1}(0.95)$ where erf−1(x) is the inverse error function Real number $z$ such that ${\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{z}e^{-x^{2}/2}\,\mathrm {d} x=0.975$	১৯২৫
লেণ্ডাউৰ ধ্ৰুৱক	$L$	$0.5<L\leq 0.54326$	The best known bounds are $0.5<L\leq {\frac {\Gamma ({\frac {1}{3}})\Gamma ({\frac {5}{6}})}{\Gamma ({\frac {1}{6}})}}$	১৯২৯
লেণ্ডাউৰ তৃতীয় ধ্ৰুৱক	$A$	$0.5<A\leq 0.7853$		১৯২৯
Prouhet–Thue–Morse constant	$\tau$	0.41245 40336 40107 59778	$\sum _{n=0}^{\infty }{\frac {t_{n}}{2^{n+1}}}={\frac {1}{4}}\left[2-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2^{n}}}}\right)\right]$ where ${t_{n}}$ is the nth term of the Thue–Morse sequence	১৯২৯	$\mathbb {R} \setminus \mathbb {A}$
Golomb–Dickman constant	$\lambda$	0.62432 99885 43550 87099	$\int _{0}^{1}e^{\mathrm {Li} (t)}dt=\int _{0}^{\infty }{\frac {\rho (t)}{t+2}}dt$ where Li(t) is the logarithmic integral, and ρ(t) is the Dickman function	১৯৩০ & ১৯৬৪
Constant related to the asymptotic behavior of Lebesgue constants	$c$	0.98943 12738 31146 95174	$\lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)$	১৯৩০
Feller–Tornier constant	${\mathcal {C}}_{\mathrm {FT} }$	0.66131 70494 69622 33528	${{\frac {1}{2}}\prod _{p{\text{ prime}}}\left(1-{\frac {2}{p^{2}}}\right)+{\frac {1}{2}}}={\frac {3}{\pi ^{2}}}\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p^{2}-1}}\right)+{\frac {1}{2}}$	১৯৩২
Base 10 Champernowne constant	$C_{10}$	0.12345 67891 01112 13141	Defined by concatenating representations of successive integers: 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...	১৯৩৩	$\mathbb {R} \setminus \mathbb {A}$
Salem constant	$\sigma _{10}$	1.17628 08182 59917 50654	Largest real root of $x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1=0$	১৯৩৩	$\mathbb {A}$
Khinchin's constant	$K_{0}$	2.68545 20010 65306 44530	$\prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\log _{2}(n)}$	১৯৩৪
Lévy's constant (1)	$\beta$	1.18656 91104 15625 45282	${\frac {\pi ^{2}}{12\,\ln 2}}$	১৯৩৫
Lévy's constant (2)	$e^{\beta }$	3.27582 29187 21811 15978	$e^{\pi ^{2}/(12\ln 2)}$	১৯৩৬
Copeland–Erdős constant	${\mathcal {C}}_{CE}$	0.23571 11317 19232 93137	Defined by concatenating representations of successive prime numbers: 0.2 3 5 7 11 13 17 19 23 29 31 37 ...	১৯৪৬	$\mathbb {R} \setminus \mathbb {Q}$
Mills' constant	$A$	1.30637 78838 63080 69046	Smallest positive real number A such that $\lfloor A^{3^{n}}\rfloor$ is prime for all positive integers n	১৯৪৭
Gompertz constant	$\delta$	0.59634 73623 23194 07434	$\int _{0}^{\infty }\!\!{\frac {e^{-x}}{1+x}}\,dx=\!\!\int _{0}^{1}\!\!{\frac {dx}{1-\ln x}}={\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {1}{1+{\tfrac {2}{1+{\tfrac {2}{1+{\tfrac {3}{1+3{/\cdots }}}}}}}}}}}}}$	১৯৪৮ চনৰ আগত
de Bruijn–Newman constant	$\Lambda$	$0\leq \Lambda \leq 0.2$	The number Λ where for where $H(\lambda ,z)=\int _{0}^{\infty }e^{\lambda u^{2}}\Phi (u)\cos(zu)du$ has real zeros if and only if λ ≥ Λ. where $\Phi (u)=\sum _{n=1}^{\infty }(2\pi ^{2}n^{4}e^{9u}-3\pi n^{2}e^{5u})e^{-\pi n^{2}e^{4u}}$.	১৯৫০
Van der Pauw constant	${\frac {\pi }{\ln 2}}$	4.53236 01418 27193 80962		১৯৫৮ চনৰ আগত	$\mathbb {R} \setminus \mathbb {Q}$
Magic angle	$\theta _{\mathrm {m} }$	0.95531 66181 245092 78163	$\arctan {\sqrt {2}}=\arccos {\tfrac {1}{\sqrt {3}}}\approx \textstyle {54.7356}^{\circ }$	১৯৫৯ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
Artin's constant	$C_{\mathrm {Artin} }$	0.37395 58136 19202 28805	$\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p(p-1)}}\right)$	১৯৬১ চনৰ আগত
Porter's constant	$C$	1.46707 80794 33975 47289	${\frac {6\ln 2}{\pi ^{2}}}\left(3\ln 2+4\,\gamma -{\frac {24}{\pi ^{2}}}\,\zeta '(2)-2\right)-{\frac {1}{2}}$ where γ is the Euler–Mascheroni constant and ζ '(2) is the derivative of the Riemann zeta function evaluated at s = 2	১৯৬১
Lochs constant	$L$	0.97027 01143 92033 92574	${\frac {6\ln 2\ln 10}{\pi ^{2}}}$	১৯৬৪
DeVicci's tesseract constant		1.00743 47568 84279 37609	The largest cube that can pass through in an 4D hypercube. Positive root of $4x^{8}{-}28x^{6}{-}7x^{4}{+}16x^{2}{+}16=0$	১৯৬৬	$\mathbb {A}$
Lieb's square ice constant		1.53960 07178 39002 03869	$\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}$	১৯৬৭	$\mathbb {A}$
Niven's constant	$C$	1.70521 11401 05367 76428	$1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)$	১৯৬৯
Stephens' constant		0.57595 99688 92945 43964	$\prod _{p{\text{ prime}}}\left(1-{\frac {p}{p^{3}-1}}\right)$	১৯৬৯
Regular paperfolding sequence	$P$	0.85073 61882 01867 26036	$\sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}$	১৯৭০	$\mathbb {R} \setminus \mathbb {A}$
Reciprocal Fibonacci constant	$\psi$	3.35988 56662 43177 55317	$\sum _{n=1}^{\infty }{\frac {1}{F_{n}}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{5}}+{\frac {1}{8}}+{\frac {1}{13}}+\cdots$ where Fn is the nth Fibonacci number	১৯৭৪	$\mathbb {R} \setminus \mathbb {Q}$
Chvátal–Sankoff constant for the binary alphabet	$\gamma _{2}$	$0.788071\leq \gamma _{2}\leq 0.826280$	$\lim _{n\to \infty }{\frac {\operatorname {E} [\lambda _{n,2}]}{n}}$ where E[λn,2] is the expected longest common subsequence of two random length-n binary strings	১৯৭৫
Feigenbaum constant δ	$\delta$	4.66920 16091 02990 67185	$\lim _{n\to \infty }{\frac {x_{n+1}-x_{n}}{x_{n+2}-x_{n+1}}}$ where the sequence xn is given by $x_{n+1}=ax_{n}(1-x_{n})$	১৯৭৫
Chaitin's constants	$\Omega$	In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844.	$\sum _{p\in P}2^{-|p|}$ p: Halted program সাঁচ:Abs: Size in bits of program p P: Domain of all programs that stop. অতিৰিক্ত তথ্য: Halting problem	১৯৭৫	$\mathbb {R} \setminus \mathbb {A}$
Robbins constant	$\Delta (3)$	0.66170 71822 67176 23515	${\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}$	১৯৭৭	$\mathbb {R} \setminus \mathbb {A}$
Weierstrass constant		0.47494 93799 87920 65033	${\frac {2^{5/4}{\sqrt {\pi }}\,e^{\pi /8}}{\Gamma ({\frac {1}{4}})^{2}}}$	১৯৭৮ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
Fransén–Robinson constant	$F$	2.80777 02420 28519 36522	$\int _{0}^{\infty }{\frac {dx}{\Gamma (x)}}=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx$	১৯৭৮
Feigenbaum constant α	$\alpha$	2.50290 78750 95892 82228	Ratio between the width of a tine and the width of one of its two subtines in a bifurcation diagram	১৯৭৯
Second du Bois-Reymond constant	$C_{2}$	0.19452 80494 65325 11361	${\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{2}}\right|\,dt-1$	১৯৮৩	$\mathbb {R} \setminus \mathbb {A}$
Erdős–Tenenbaum–Ford constant	$\delta$	0.08607 13320 55934 20688	$1-{\frac {1+\log \log 2}{\log 2}}$	১৯৮৪
Conway's constant	$\lambda$	1.30357 72690 34296 39125	Real root of the polynomial: ${\begin{smallmatrix}x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}$	১৯৮৭	$\mathbb {A}$
Hafner–Sarnak–McCurley constant	$\sigma$	0.35323 63718 54995 98454	$\prod _{p{\text{ prime}}}{\left(1-\left(1-\prod _{n\geq 1}\left(1-{\frac {1}{p^{n}}}\right)\right)^{2}\right)}\!$	১৯৯১
Backhouse's constant	$B$	1.45607 49485 82689 67139	$\lim _{k\to \infty }\left|{\frac {q_{k+1}}{q_{k}}}\right\vert \quad \scriptstyle {\text{where:}}\displaystyle \;\;Q(x)={\frac {1}{P(x)}}=\!\sum _{k=1}^{\infty }q_{k}x^{k}$ $P(x)=1+\sum _{k=1}^{\infty }{p_{k}x^{k}}=1+2x+3x^{2}+5x^{3}+\cdots$where pk is the kth prime number	১৯৯৫
Viswanath constant		1.13198 82487 943	$\lim _{n\to \infty }|f_{n}|^{\frac {1}{n}}$      where fn = fn−1 ± fn−2, where the signs + or − are chosen at random with equal probability 1/2	১৯৯৭
Komornik–Loreti constant	$q$	1.78723 16501 82965 93301	Real number $q$ such that $1=\sum _{k=1}^{\infty }{\frac {t_{k}}{q^{k}}}$, or $\prod _{n=0}^{\infty }\left(1-{\frac {1}{q^{2^{n}}}}\right)+{\frac {q-2}{q-1}}=0$ where tk is the kth term of the Thue–Morse sequence	১৯৯৮	$\mathbb {R} \setminus \mathbb {A}$
Embree–Trefethen constant	$\beta ^{\star }$	0.70258		১৯৯৯
Heath-Brown–Moroz constant	$C$	0.00131 76411 54853 17810	$\prod _{p{\text{ prime}}}\left(1-{\frac {1}{p}}\right)^{7}\left(1+{\frac {7p+1}{p^{2}}}\right)$	১৯৯৯
এমআৰবি ধ্ৰুৱক	$S$	0.18785 96424 62067 12024	$\sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots$	১৯৯৯
মৌলিক ধ্ৰুৱক	$\rho$	০.৪১৪৬৮ ২৫০৯৮ ৫১১১১ ৬৬০২৪	$\sum _{p{\text{ prime}}}{\frac {1}{2^{p}}}={\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{32}}+\cdots$	১৯৯৯	$\mathbb {R} \setminus \mathbb {Q}$
Somos' quadratic recurrence constant	$\sigma$	1.66168 79496 33594 12129	$\prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots$	১৯৯৯
Foias constant	$\alpha$	1.18745 23511 26501 05459	$x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}{\text{ for }}n=1,2,3,\ldots$ Foias constant is the unique real number such that if x1 = α then the sequence diverges to infinity	২০০০
Logarithmic capacity of the unit disk		০.৫৯০১৭ ০২৯৯৫ ০৮০৪৮ ১১৩০২	${\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}$	২০০৩ চনৰ আগত	$\mathbb {R} \setminus \mathbb {A}$
টানিগুছি ধ্ৰুৱক		০.৬৭৮২৩ ৪৪৯১৯ ১৭৩৯১ ৯৭৮০৩	$\prod _{p{\text{ prime}}}\left(1-{\frac {3}{p^{3}}}+{\frac {2}{p^{4}}}+{\frac {1}{p^{5}}}-{\frac {1}{p^{6}}}\right)$	২০০৫ চনৰ আগত

ধ্ৰুৱকৰ অনুক্ৰম

নাম	চিহ্ন	সূত্ৰ	বৰ্ষ	সংহতি
হৰাত্মক সংখ্যা	$H_{n}$	$\sum _{k=1}^{n}{\frac {1}{k}}$	প্ৰাচীন	$\mathbb {Q}$
গ্ৰেগ'ৰি গুণাংক	$G_{n}$	${\frac {1}{n!}}\int _{0}^{1}x(x-1)(x-2)\cdots (x-n+1)\,dx=\int _{0}^{1}{\binom {x}{n}}\,dx$	১৬৭০	$\mathbb {Q}$
বাৰ্ণ'লি সংখ্যা	$B_{n}^{\pm }$	${\frac {t}{2}}\left(\operatorname {coth} {\frac {t}{2}}\pm 1\right)=\sum _{m=0}^{\infty }{\frac {B_{m}^{\pm {}}t^{m}}{m!}}$	১৬৮৯	$\mathbb {Q}$
হাৰমাইট ধ্ৰুৱক	$\gamma _{n}$	For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let λ1(L) denote the least length of a nonzero element of L. Then √γসাঁচ:Subscriptn is the maximum of λ1(L) over all such lattices L.	১৮২২ – ১৯০১	$\mathbb {R}$
হফনাৰ–ছৰনাক–মেককাৰ্লি ধ্ৰুৱক	$D(n)$	$D(n)=\prod _{k=1}^{\infty }\left\{1-\left[1-\prod _{j=1}^{n}(1-p_{k}^{-j})\right]^{2}\right\}$	১৮৮৩	$\mathbb {R}$
ষ্টীলজেছ ধ্ৰুৱক	$\gamma _{n}$	${\frac {(-1)^{n}n!}{2\pi }}\int _{0}^{2\pi }e^{-nix}\zeta \left(e^{ix}+1\right)dx.$	১৮৯৪ চনৰ আগত	$\mathbb {R}$
ফাভাৰ্ড ধ্ৰুৱক	$K_{r}$	${\frac {4}{\pi }}\sum _{n=0}^{\infty }\left({\frac {(-1)^{n}}{2n+1}}\right)^{\!r+1}={\frac {4}{\pi }}\left({\frac {(-1)^{0(r+1)}}{1^{r}}}+{\frac {(-1)^{1(r+1)}}{3^{r}}}+{\frac {(-1)^{2(r+1)}}{5^{r}}}+{\frac {(-1)^{3(r+1)}}{7^{r}}}+\cdots \right)$	১৯০২ – ১৯৬৫	$\mathbb {R}$
সাধাৰণীকৃত ব্ৰুণৰ ধ্ৰুৱক	$B_{n}$	${\sum \limits _{p}({\frac {1}{p}}+{\frac {1}{p+n}})}$ where the sum ranges over all primes p such that p + n is also a prime	১৯১৯	$\mathbb {R}$
Champernowne constants	$C_{b}$	Defined by concatenating representations of successive integers in base b. $C_{b}=\sum _{n=1}^{\infty }{\frac {n}{b^{\left(\sum _{k=1}^{n}\lceil \log _{b}(k+1)\rceil \right)}}}$	১৯৩৩	$\mathbb {R} \setminus \mathbb {A}$
লাগ্ৰাঞ্জ সংখ্যা	$L(n)$	${\sqrt {9-{\frac {4}{{m_{n}}^{2}}}}}$ where $m_{n}$ is the nth smallest number such that $m^{2}+x^{2}+y^{2}=3mxy\,$ has positive (x,y).	১৯৫৭ চনৰ আগত	$\mathbb {A}$
Feller's coin-tossing constants	$\alpha _{k},\beta _{k}$	$\alpha _{k}$ is the smallest positive real root of $x^{k+1}=2^{k+1}(x-1),\beta _{k}={\frac {2-\alpha _{k}}{k+1-k\alpha _{k}}}$	১৯৬৮	$\mathbb {A}$
Stoneham number	$\alpha _{b,c}$	$\sum _{n=c^{k}>1}{\frac {1}{b^{n}n}}=\sum _{k=1}^{\infty }{\frac {1}{b^{c^{k}}c^{k}}}$ where b,c are coprime integers.	১৯৭৩	$\mathbb {R} \setminus \mathbb {Q}$
Beraha constants	$B(n)$	$2+2\cos \left({\frac {2\pi }{n}}\right)$	১৯৭৪	$\mathbb {A}$
Chvátal–Sankoff constants	$\gamma _{k}$	$\lim _{n\to \infty }{\frac {E[\lambda _{n,k}]}{n}}$	১৯৭৫	$\mathbb {R}$
Hyperharmonic number	$H_{n}^{(r)}$	$\sum _{k=1}^{n}H_{k}^{(r-1)}$ and $H_{n}^{(0)}={\frac {1}{n}}$	১৯৯৫	$\mathbb {Q}$
গ্ৰেগ'ৰি সংখ্যা	$G_{x}$	$\sum _{n=0}^{\infty }(-1)^{n}{\frac {1}{(2n+1)x^{2n+1}}}$ for rational x greater than one.	১৯৯৬ চনৰ আগত	$\mathbb {R}$
Metallic mean		${\frac {n+{\sqrt {n^{2}+4}}}{2}}$	১৯৯৮ চনৰ আগত	$\mathbb {A}$

তথ্যসূত্ৰ

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OEIS.org

OEIS Wiki

গ্ৰন্থপঞ্জী

• Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. https://books.google.com/books?id=QwwcmweJCDQC। আহৰণ কৰা হৈছে: 2013-06-05.  English translation by Catriona and David Lischka.
• Jensen, Johan Ludwig William Valdemar (1895), "Note numéro 245. Deuxième réponse. Remarques relatives aux réponses du MM. Franel et Kluyver", L'Intermédiaire des Mathématiciens খণ্ড II: 346–347 
• "Mathematical constants". Handbook of Continued Fractions for Special Functions. প্ৰকাশক Dordrecht, Netherlands: Springer Science + Business Media. 2008. ISBN 9781402069499. 
• Neverending Fractions: An Introduction to Continued Fractions. Australian Mathematical Society Lecture Series. 23. প্ৰকাশক Cambridge, United Kingdom: Cambridge University Press. 2014. ISBN 9780521186490. ISSN 0950-2815.