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 A020759 #63 Nov 19 2024 08:55:54
%S A020759 1,9,6,3,5,1,0,0,2,6,0,2,1,4,2,3,4,7,9,4,4,0,9,7,6,3,3,2,9,9,8,7,5,5,
%T A020759 5,6,7,1,9,3,1,5,9,6,0,4,6,6,0,4,3,4,1,0,7,0,4,7,1,2,7,2,5,3,8,7,1,6,
%U A020759 5,4,9,7,0,7,1,7,0,5,4,1,0,2,1,4,8,6,7,3,7,1,7,2,8,4,5,8,4,1,2,4,5,9,8,6,3
%N A020759 Decimal expansion of (-1)*Gamma'(1/2)/Gamma(1/2) where Gamma(x) denotes the Gamma function.
%C A020759 Decimal expansion of -psi(1/2). - _Benoit Cloitre_, Mar 07 2004
%D A020759 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), 6.3.3, p. 258. - _Robert G. Wilson v_, Jun 20 2011
%D A020759 S. J. Patterson, An introduction to the theory of the Riemann zeta function, Cambridge studies in advanced mathematics no. 14, p. 135.
%H A020759 Vincenzo Librandi, <a href="/A020759/b020759.txt">Table of n, a(n) for n = 1..1000</a>
%H A020759 Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
%H A020759 <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a>.
%F A020759 Gamma'(1/2)/Gamma(1/2) = -EulerGamma - 2*log(2) = -1.9635100260214234794... where EulerGamma is the Euler-Mascheroni constant (A001620).
%F A020759 Equals 2 - psi(-1/2) = 2-A248176. - _Stanislav Sykora_, Oct 03 2014
%F A020759 Equals A131265/A002161. - _R. J. Mathar_, Jun 02 2022
%F A020759 Equals lim_{n->oo} (Sum_{k=0..n} 1/(k+1/2) - log(n)). - _Amiram Eldar_, Mar 04 2023
%e A020759 1.96351002602142347944097633299875556719315960466...
%p A020759 evalf(-Psi(0.5)) ; # _R. J. Mathar_, Sep 10 2013
%t A020759 RealDigits[ EulerGamma + 2 Log[2], 10, 111][[1]] (* _Robert G. Wilson v_, Jun 20 2011 *)
%o A020759 (PARI) Euler+2*log(2)
%o A020759 (PARI) 2-psi(-1/2) \\ _Stanislav Sykora_, Oct 03 2014
%o A020759 (Magma) R:=RealField(100); EulerGamma(R) + 2*Log(2); // _G. C. Greubel_, Aug 27 2018
%Y A020759 Cf. A001620, A002161, A002162, A131265, A248176.
%K A020759 cons,nonn
%O A020759 1,2
%A A020759 _Benoit Cloitre_, May 24 2003