অসমীয়া বিশ্বকোষঅসম আৰু অসমীয়া ভাষাৰ জ্ঞানকোষ
অৱদান
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গাণিতিক ধ্ৰুৱকৰ তালিকা

__NOTOC__গাণিতিক ধ্ৰুৱক 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।

অসমীয়া ৱিকিপিডিয়াৰ অৱদানকাৰীসকল হালনাগাদ: ১ নৱেম্বৰ ২০২৬ ১৩৪ শব্দ · ১ মিনিট সংগৃহীত ৮০
সংশোধনৰ পৰামৰ্শ

গাণিতিক ধ্ৰুৱক 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

নামচিহ্নদশমিক প্ৰসাৰণসূত্ৰবৰ্ষসংহতি
এক১১প্ৰাক‌ঐতিহাসিক⟨\mathbb{N}⟩
দুই২২প্ৰাক‌ঐতিহাসিক⟨\mathbb{N}⟩
আধা১/২০.৫প্ৰাক‌ঐতিহাসিক⟨\mathbb{Q}⟩
পাই⟨\pi⟩৩.১৪১৫৯ ২৬৫৩৫ ৮৯৭৯৩এটা বৃত্তৰ পৰিধি আৰু ব্যাসৰ অনুপাত।খ্ৰীষ্টাব্দ ১৯০০ – ১৬০০১⟨\mathbb{R} \setminus \mathbb{A}⟩
টাউ (গাণিতিক ধ্ৰুৱক)⟨\tau⟩৬.২৮৩১৮ ৫৩০৭১ ৭৯৫৮৬ ৪৭৬৯২২এটা বৃত্তৰ পৰিধি আৰু ইয়াৰ ব্যাসাৰ্ধৰ অনুপাত। ⟨2\pi⟩ ৰ সমতুল্য।খ্ৰীষ্টাব্দ ১৯০০ – ১৬০০১⟨\mathbb{R} \setminus \mathbb{A}⟩
দুইৰ বৰ্গমূল, পাইথেগাৰাছৰ ধ্ৰুৱক৩⟨\sqrt{2}⟩১.৪১৪২১ ৩৫৬২৩ ৭৩০৯৫ ০৪৮৮০⟨x^2=2⟩ ৰ ধনাত্মক মূল।খ্ৰীষ্টাব্দ ১৮০০ – ১৬০০৪⟨\mathbb{A}⟩
৩ ৰ বৰ্গমূল, থিঅ'ডৰাছৰ ধ্ৰুৱক৫⟨\sqrt{3}⟩১.৭৩২০৫ ০৮০৭৫ ৬৮৮৭৭ ২৯৩৫২⟨x^2=3⟩ ৰ ধনাত্মক মূল।খ্ৰীষ্টাব্দ ৪৬৫ – ৩৯৮⟨\mathbb{A}⟩
৫ ৰ বৰ্গমূল৬⟨\sqrt{5}⟩২.২৩৬০৬ ৭৯৭৭৪ ৯৯৭৮৯ ৬৯৬৪০⟨x^2=5⟩ ৰ ধনাত্মক মূল।⟨\mathbb{A}⟩
ফাই, সোণালী অনুপাত৭⟨\varphi⟩ বা ⟨\phi⟩১.৬১৮০৩ ৩৯৮৮৭ ৪৯৮৯৪ ৮৪৮২০⟨\frac{1+\sqrt{5{2}⟩খ্ৰীষ্টাব্দ ~৩০০⟨\mathbb{A}⟩
ৰূপালী অনুপাত৮⟨\delta_S⟩২.৪১৪২১ ৩৫৬২৩ ৭৩০৯৫ ০৪৮৮০⟨\sqrt{2}+1⟩খ্ৰীষ্টাব্দ ~৩০০⟨\mathbb{A}⟩
শূন্য০০খ্ৰীষ্টাব্দ ৩০০ – ১০০৯⟨\mathbb{Z}⟩
ঋণাত্মক এক−১−১খ্ৰীষ্টাব্দ ৩০০ – ২০০⟨\mathbb{Z}⟩
২ ৰ ঘনমূল⟨\sqrt[3]{2}⟩১.২৫৯৯২ ১০৪৯৮ ৯৪৮৭৩ ১৬৪৭৬⟨x^3=2⟩ ৰ প্ৰকৃত মূল।৪৬ – ১২০ খ্ৰীষ্টাব্দ১০⟨\mathbb{A}⟩
৩ ৰ ঘনমূল⟨\sqrt[3]{3}⟩১.৪৪২২৪ ৯৫৭০৩ ০৭৪০৮ ৩৮২৩২⟨x^3=3⟩ ৰ প্ৰকৃত মূল।⟨\mathbb{A}⟩
Twelfth root of 2১১⟨\sqrt[12]{2}⟩1.05946 30943 59295 26456⟨x^{12}=2⟩ ৰ প্ৰকৃত মূল।⟨\mathbb{A}⟩
Supergolden ratio১২⟨\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 একক১৩⟨i⟩Either of the two roots of ⟨x^2=-1⟩১৫০১ – ১৫৭৬⟨\mathbb{C}⟩
হেক্সাগনেল লেটিচৰ বাবে সংযোগী ধ্ৰুৱক১৪১৫⟨\mu⟩1.84775 90650 22573 51225⟨\sqrt{2 + \sqrt{2⟩, as a root of the polynomial ⟨x ^ 4-4 x ^ 2 + 2=0⟩১৫৯৩⟨\mathbb{A}⟩
কেপলাৰ-বাউকেম্প ধ্ৰুৱক১৬⟨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 ধ্ৰুৱক2.09455 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 সংখ্যা১৭⟨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⟩১৬১৮১৮⟨\mathbb{R} \setminus \mathbb{A}⟩
২ ৰ স্বাভাৱিক ঘাতাংক১৯⟨\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⟩১৬১৯২০ আৰু ১৬৬৮২১⟨\mathbb{R} \setminus \mathbb{A}⟩
Lemniscate constant২২⟨\varpi⟩2.62205 75542 92119 81046⟨\pi \, {G} = 4 \sqrt{\tfrac2\pi}\,\Gamma{\left(\tfrac54 \right)^2} = \tfrac14 \sqrt{\tfrac{2}{\pi\,\Gamma {\left(\tfrac14 \right)^2}⟩ where ⟨G⟩ is Gauss's constant১৭১৮ – 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 \frac1{k}\right)=\int_1^\infty\left(-\frac1x+\frac1{\lfloor x\rfloor}\right)\,dx⟩১৭৩৫
Erdős–Borwein constant২৩⟨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⟩১৭৪৯২৪⟨\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 function১৭৫৮ আৰু ১৭৮৩⟨\mathbb{R} \setminus \mathbb{A}⟩
Apéry's constant২৫⟨\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 সীমা২৬0.66274 34193 49181 58097Real root of ⟨\frac{ x e^\sqrt{x^2+1{\sqrt{x^2+1}+1} = 1⟩~১৭৮২⟨\mathbb{R} \setminus \mathbb{A}⟩
Ramanujan–Soldner constant২৭২৮⟨\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 ধ্ৰুৱক২৯⟨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 mean১৭৯৯৩০⟨\mathbb{R} \setminus \mathbb{A}⟩
দ্বিতীয় হাৰমাইট ধ্ৰুৱক৩১⟨\gamma_{2}⟩1.15470 05383 79251 52901⟨\frac{2}{\sqrt{3⟩১৮২২ – ১৯০১⟨\mathbb{A}⟩
Liouville's constant৩২⟨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 function১৮৫৫৩৩⟨\mathbb{R} \setminus \mathbb{Q}⟩
ৰামানুজনৰ ধ্ৰুৱক৩৪262 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 constant৩৫৩৬৩৭⟨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 number৩৮0.73908 51332 15160 64165Real root of ⟨\cos x = x⟩১৮৬৫⟨\mathbb{R} \setminus \mathbb{A}⟩
Meissel–Mertens constant৩৯⟨M⟩0.26149 72128 47642 78375⟨\lim_{n\to\infty}\left(\sum_{p\le 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 prime১৮৬৬ আৰু ১৮৭৩
Universal parabolic constant৪০⟨P⟩2.29558 71493 92638 07403⟨\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arsinh}(1)+\sqrt{2}⟩১৮৯১ চনৰ আগত৪১⟨\mathbb{R} \setminus \mathbb{A}⟩
Cahen's constant৪২⟨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 constant৪৩⟨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⟩১৯০০৪৪⟨\mathbb{R} \setminus \mathbb{A}⟩
Gelfond–Schneider constant৪৫⟨2^{\sqrt{2⟩2.66514 41426 90225 18865১৯০২ চনৰ আগত⟨\mathbb{R} \setminus \mathbb{A}⟩
Second Favard constant৪৬⟨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 কোণ৪৭⟨g⟩2.39996 32297 28653 32223⟨\frac{2\pi}{\varphi^2} = \pi (3-\sqrt{5})⟩ or ⟨180 (3-\sqrt{5})=137.50776\ldots⟩ in degrees১৯০৭⟨\mathbb{R} \setminus \mathbb{A}⟩
Sierpiński's constant৪৮⟨K⟩2.58498 17595 79253 21706⟨\begin{align} &\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{align}⟩১৯০৭
লেণ্ডাউ-ৰামানুজন ধ্ৰুৱক৪৯⟨K⟩0.76422 36535 89220 66299⟨\frac1{\sqrt2}\prod_ {\left(1-\frac1{p^2}\right)^{-\frac{1}{2}\!\!=\frac\pi4\prod_ {\left(1-\frac1{p^2}\right)^\frac{1}{2⟩১৯০৮
First Nielsen–শ্ৰীনিবাস ৰামানুজন constant৫০⟨a_{1}⟩0.82246 70334 24113 21823⟨\frac{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 constant৫১⟨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 ধ্ৰুৱক৫২⟨\beta⟩0.28016 94990 23869 13303⟨\lim_{n\to\infty} 2n E_{2n}(f)⟩, where E'n(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 ধ্ৰুৱক৫৩1.83928 67552 14161 13255⟨\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 constant৫৪⟨B_{2}⟩1.90216 05831 04⟨\textstyle {\sum\limits_p(\frac1{p}+\frac1{p+2})} = (\frac1{3} \! + \! \frac1{5}) + (\tfrac1{5} \! + \! \tfrac1{7}) + (\tfrac1{11} \! + \! \tfrac1{13}) + \cdots⟩ where the sum ranges over all primes p such that p + 2 is also a prime১৯১৯
Twin primes constant⟨C_{2}⟩0.66016 18158 46869 57392⟨\prod_{\textstyle{p\;{\rm prime}\atop p \ge 3 \left(1 - \frac{1}{(p-1)^2}\right)⟩১৯২২
প্লাষ্টিক অনুপাত৫৫⟨\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 constant৫৬⟨B⟩⟨0.4332\leq B\leq 0.4719⟩The best known bounds are ⟨\frac{\sqrt{3{4}+2\times10^{-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 point৫৭৫৮৫৯৬০⟨z_{.975}⟩1.95996 39845 40054 23552⟨\sqrt{2}\operatorname{erf}^{-1}(0.95)⟩ where 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 ধ্ৰুৱক৫৬⟨L⟩⟨0.5 < L \le 0.54326⟩The best known bounds are ⟨0.5 < L \le \frac{\Gamma(\frac{1}{3})\Gamma(\frac{5}{6})}{\Gamma(\frac{1}{6})}⟩১৯২৯
লেণ্ডাউৰ তৃতীয় ধ্ৰুৱক৫৬⟨A⟩⟨0.5 < A \le 0.7853⟩১৯২৯
Prouhet–Thue–Morse constant৬১⟨\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 sequence১৯২৯⟨\mathbb{R} \setminus \mathbb{A}⟩
Golomb–Dickman constant৬২⟨\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 function১৯৩০ & ১৯৬৪
Constant related to the asymptotic behavior of Lebesgue constants৬৩⟨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'(\tfrac12)}{\Gamma(\tfrac12)}\!\!\right)⟩১৯৩০
Feller–Tornier constant৬৪⟨\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 constant৬৫⟨C_{10}⟩0.12345 67891 01112 13141Defined 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 constant৬৬⟨\sigma_{10}⟩1.17628 08182 59917 50654Largest 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 constant৬৭⟨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)৬৮⟨\beta⟩1.18656 91104 15625 45282⟨\frac {\pi^2}{12\,\ln 2}⟩১৯৩৫
Lévy's constant (2)৬৯⟨e^{\beta}⟩3.27582 29187 21811 15978⟨e^{\pi^2/(12\ln2)}⟩১৯৩৬
Copeland–Erdős constant৭০⟨\mathcal{C}_{CE}⟩0.23571 11317 19232 93137Defined 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' constant৭১⟨A⟩1.30637 78838 63080 69046Smallest positive real number A such that ⟨\lfloor A^{3^{n \rfloor⟩ is prime for all positive integers n১৯৪৭
Gompertz constant৭২⟨\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\le\Lambda\le0.2⟩The number Λ where for where ⟨H(\lambda,z)=\int^{\infty}_0e^{\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^2n^4e^{9u}-3\pi n^2e^{5u})e^{-\pi n^2e^{4u⟩.১৯৫০
Van der Pauw constant⟨\frac{\pi}{\ln 2}⟩4.53236 01418 27193 80962১৯৫৮ চনৰ আগত⟨\mathbb{R} \setminus \mathbb{Q}⟩
Magic angle৭৩⟨\theta_{\mathrm{m⟩0.95531 66181 245092 78163⟨\arctan \sqrt{2} = \arccos \tfrac{1}{\sqrt 3} \approx \textstyle {54.7356} ^{ \circ }⟩১৯৫৯ চনৰ আগত৭৪৭৩⟨\mathbb{R} \setminus \mathbb{A}⟩
Artin's constant৭৫⟨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 constant৭৬⟨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 is the derivative of the Riemann zeta function evaluated at s = 2১৯৬১
Lochs constant৭৭⟨L⟩0.97027 01143 92033 92574⟨\frac {6 \ln 2 \ln 10}{ \pi^2}⟩১৯৬৪
DeVicci's tesseract constant1.00743 47568 84279 37609The 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 constant৭৮1.53960 07178 39002 03869⟨\left(\frac{4}{3}\right)^\frac{3}{2}=\frac{8}{3\sqrt3}⟩১৯৬৭⟨\mathbb{A}⟩
Niven's constant৭৯⟨C⟩1.70521 11401 05367 76428⟨1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)⟩১৯৬৯
Stephens' constant৮০0.57595 99688 92945 43964⟨\prod_{p\text{ prime \left(1 - \frac{p}{p^3-1}\right)⟩১৯৬৯
Regular paperfolding sequence৮১৮২⟨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 constant৮৩⟨\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 number১৯৭৪⟨\mathbb{R} \setminus \mathbb{Q}⟩
Chvátal–Sankoff constant for the binary alphabet⟨\gamma_2⟩⟨0.788071 \le \gamma_2 \le 0.826280⟩⟨\lim_{n\to\infty}\frac{\operatorname{E}[\lambda_{n,2}]}{n}⟩ where is the expected Longest common subsequence of two random length-n binary strings১৯৭৫
Feigenbaum constant δ ৮৪⟨\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 ৮৫⟨\Omega⟩In general they are Uncomputable numbers. But one such number is 0.00787 49969 97812 3844.⟨\sum_{p \in P} 2^{-|p|}⟩ *: Halted program *: Size in bits of program *: Domain of all programs that stop. লগতে চাওক: Halting problem১৯৭৫⟨\mathbb{R} \setminus \mathbb{A}⟩
Robbins constant৮৬⟨\Delta(3)⟩0.66170 71822 67176 23515⟨\frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5}⟩১৯৭৭⟨\mathbb{R} \setminus \mathbb{A}⟩
Weierstrass constant ৮৭0.47494 93799 87920 65033⟨\frac{2^{5/4} \sqrt{\pi} \, e^{\pi/8{\Gamma(\frac{1}{4})^{2⟩১৯৭৮ চনৰ আগত৮৮⟨\mathbb{R} \setminus \mathbb{A}⟩
Fransén–Robinson constant৮৯⟨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 α৯০⟨\alpha⟩2.50290 78750 95892 82228Ratio between the width of a tine and the width of one of its two subtines in a Bifurcation diagram১৯৭৯
Second du Bois-Reymond constant৯১⟨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\log2}{\log2}⟩১৯৮৪
Conway's constant৯২⟨\lambda⟩1.30357 72690 34296 39125Real 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 constant৯৩⟨\sigma⟩0.35323 63718 54995 98454⟨\prod_{p\text{ prime{\left(1- \left(1-\prod_{n\ge1}\left(1-\frac{1}{p^n}\right)\right)^2 \right)} \!⟩১৯৯১
Backhouse's constant৯৪⟨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 number১৯৯৫
Viswanath constant৯৫1.13198 82487 943⟨\lim_{n \to \infty}|f_n|^\frac{1}{n}⟩ where fn = fn−1 ± f'n''−2, where the signs + or − are chosen at random with equal probability 1/2১৯৯৭
Komornik–Loreti constant৯৬⟨q⟩1.78723 16501 82965 93301Real 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 sequence১৯৯৮⟨\mathbb{R} \setminus \mathbb{A}⟩
Embree–Trefethen constant⟨\beta^{\star}⟩0.70258১৯৯৯
Heath-Brown–Moroz constant৯৭⟨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 ধ্ৰুৱক৯৮৯৯১০০⟨S⟩0.18785 96424 62067 12024 ১০১⟨\sum_{n=1}^{\infty} (-1)^n (n^{1/n}-1) = - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \cdots⟩১৯৯৯
মৌলিক ধ্ৰুৱক১০২⟨\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 constant১০৩⟨\sigma⟩1.66168 79496 33594 12129⟨\prod_{n=1}^\infty n^} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots⟩১৯৯৯
Foias constant১০৪⟨\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 infinity২০০০
Logarithmic capacity of the unit disk১০৫১০৬০.৫৯০১৭ ০২৯৯৫ ০৮০৪৮ ১১৩০২⟨\frac{\Gamma(\tfrac14)^2}{4 \pi^{3/2⟩২০০৩ চনৰ আগত⟨\mathbb{R} \setminus \mathbb{A}⟩
টানিগুছি ধ্ৰুৱক৮০০.৬৭৮২৩ 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 আগত৮০

ধ্ৰুৱকৰ অনুক্ৰম

নামচিহ্নসূত্ৰবৰ্ষসংহতি
হৰাত্মক সংখ্যা⟨H_n⟩⟨\sum^n_{k=1}\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^\pm_n⟩⟨\frac{t}{2} \left( \operatorname{coth} \frac{t}{2} \pm 1 \right) = \sum_{m=0}^\infty \frac{B^{\pm{_m t^m}{m!}⟩১৬৮৯⟨\mathbb{Q}⟩
হাৰমাইট ধ্ৰুৱক১০৭⟨\gamma_{n}⟩For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let λ(L) denote the least length of a nonzero element of L. Then √γn is the maximum of λ(L) over all such lattices L.১৮২২ – ১৯০১⟨\mathbb{R}⟩
হফনাৰ–ছৰনাক–মেককাৰ্লি ধ্ৰুৱক১০৮⟨D(n)⟩⟨D(n)= \prod^\infty_{k=1}\left\{1-\left[1-\prod^n_{j=1}(1-p_k^{-j}) \right]^2 \right\}⟩১৮৮৩⟨\mathbb{R}⟩
ষ্টীলজেছ ধ্ৰুৱক⟨\gamma_n⟩⟨{\frac {(-1)^{n}n!}{2\pi \int _{0}^e^\zeta \left(e^+1\right)dx.⟩১৮৯৪ চনৰ আগত⟨\mathbb{R}⟩
ফাভাৰ্ড ধ্ৰুৱক৪৬১০৯⟨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 ধ্ৰুৱক৫৪⟨B_{n}⟩⟨{\sum\limits_p(\frac1{p}+\frac1{p+n})}⟩ where the sum ranges over all primes p such that p + n is also a prime১৯১৯⟨\mathbb{R}⟩
Champernowne constants৬৫⟨C_{b}⟩Defined by concatenating representations of successive integers in base b. ⟨C_b=\sum^\infty_{n=1}\frac{n}{b^{\left(\sum^n_{k=1}\lceil\log_b(k+1)\rceil\right)⟩১৯৩৩⟨\mathbb{R} \setminus \mathbb{A}⟩
লাগ্ৰাঞ্জ সংখ্যা⟨L(n)⟩⟨\sqrt{9-\frac{4}⟩ 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^nn} = \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^{(r)}_n⟩⟨\sum^n_{k=1}H^{(r-1)}_k⟩ and ⟨H^{(0)}_n=\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}⟩

গ্ৰন্থপঞ্জী

  • Arndt, Jörg; Haenel, Christoph. (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4 <!--isbn only volume 1--> 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. পৃ. 346–347
  • (2008). Handbook of Continued Fractions for Special Functions. Springer Science + Business Media. ISBN 9781402069499
  • (2014). Neverending Fractions: An Introduction to Continued Fractions. Australian Mathematical Society Lecture Series. Cambridge University Press. ISBN 9780521186490

তথ্যসূত্ৰ

  1. ↑ Arndt Haenel 2006, পৃ. 167
  2. ↑ Hartl, Michael. 100,000 digits of Tau. Tau Day
  3. ↑ Calvin C Clawson. (2001). Mathematical sorcery: revealing the secrets of numbers. Basic Books. পৃ. IV. ISBN 978 0 7382 0496-3
  4. ↑ Fowler and Robson, p. 368. Photograph, illustration, and description of the root(2) tablet from the Yale Babylonian Collection High resolution photographs, descriptions, and analysis of the root(2) tablet (YBC 7289) from the Yale Babylonian Collection
  5. ↑ Vijaya AV. (2007). Figuring Out Mathematics. Dorling Kindcrsley (India) Pvt. Lid. পৃ. 15. ISBN 978-81-317-0359-5
  6. ↑ P A J Lewis. (2008). Essential Mathematics 9. Ratna Sagar. পৃ. 24. ISBN 9788183323673
  7. ↑ Timothy Gowers; June Barrow-Green; Imre Leade. (2007). The Princeton Companion to Mathematics. Princeton University Press. পৃ. 316. ISBN 978-0-691-11880-2
  8. ↑ Kapusta, Janos. (2004). The square, the circle, and the golden proportion: a new class of geometrical constructions. Forma. পৃ. 293–313
  9. ↑ Kim Plofker (2009), Mathematics in India, Princeton University Press,, pp. 54–56
  10. ↑ Plutarch. Quaestiones convivales VIII.ii
  11. ↑ Christensen, Thomas. (2002). The Cambridge History of Western Music Theory. পৃ. 205. ISBN 978-0521686983
  12. ↑ Koshy, Thomas. (2017). Fibonacci and Lucas Numbers with Applications. John Wiley & Sons. ISBN 9781118742174
  13. ↑ Keith J. Devlin. (1999). Mathematics: The New Golden Age. Columbia University Press. পৃ. 66. ISBN 978-0-231-11638-1
  14. ↑ Mireille Bousquet-Mélou. Two-dimensional self-avoiding walks. CNRS, LaBRI, Bordeaux, France
  15. ↑ Hugo Duminil-Copin; Stanislav Smirnov. (2011). The connective constant of the honeycomb lattice √ (2 + √ 2). Université de Geneve
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