This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A020777 #32 Nov 19 2024 09:03:54 %S A020777 4,2,2,7,4,5,3,5,3,3,3,7,6,2,6,5,4,0,8,0,8,9,5,3,0,1,4,6,0,9,6,6,8,3, %T A020777 5,7,7,3,6,7,2,4,4,4,3,8,7,0,8,2,4,2,2,7,1,6,5,5,2,7,9,5,5,9,5,1,8,9, %U A020777 5,6,7,9,5,8,2,9,8,5,3,3,1,7,0,6,8,5,5,4,4,5,6,9,5,2,0,6,1,3,4,6,1,3,1,7,0 %N A020777 Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where Gamma(x) denotes the Gamma function. %D A020777 S.J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135, 1995. %H A020777 G. C. Greubel, <a href="/A020777/b020777.txt">Table of n, a(n) for n = 1..10000</a> %H A020777 E. D. Krupnikov, K. S. Kölbig, <a href="https://doi.org/10.1016/S0377-0427(96)00111-2">Some special cases of the generalized hypergeometric function (q+1)Fq</a>, J. Comp. Appl. Math. 78 (1997) 79-95, psi(1/4). %H A020777 Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a> %H A020777 <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a> %F A020777 Gamma'(1/4)/Gamma(1/4) = -EulerGamma - 3*log(2) - Pi/2 where EulerGamma is the Euler-Mascheroni constant (A001620). %F A020777 Pi = gamma(0,1/4) - gamma(0,3/4) = A020777 - A200134, where gamma(n,x) denotes the generalized Stieltjes constants. - _Peter Luschny_, May 16 2018 %e A020777 4.2274535333762654080895301460966835773672444387082422716552795595189567958... %p A020777 evalf(gamma+3*log(2)+Pi/2) ; # _R. J. Mathar_, Nov 13 2011 %p A020777 evalf(abs(Psi(1/4))) ; # _R. J. Mathar_, Nov 19 2024 %t A020777 EulerGamma + Pi/2 + Log[8] // RealDigits[#, 10, 105][[1]] & (* _Jean-François Alcover_, Jun 18 2013 *) %t A020777 N[StieltjesGamma[0, 1/4], 99] (* _Peter Luschny_, May 16 2018 *) %o A020777 (PARI) Euler+3*log(2)+Pi/2 %o A020777 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R) + Pi(R)/2 + Log(8); // _G. C. Greubel_, Aug 28 2018 %Y A020777 Cf. A001620, A200134, A301816. %K A020777 cons,nonn %O A020777 1,1 %A A020777 _Benoit Cloitre_, May 24 2003