cp's OEIS Frontend

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.

A047787 Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function.

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%I A047787 #22 May 13 2024 09:32:31
%S A047787 3,1,3,2,0,3,3,7,8,0,0,2,0,8,0,6,3,2,2,9,9,6,4,1,9,0,7,4,2,8,7,2,6,8,
%T A047787 8,5,4,1,5,5,4,2,8,2,9,6,7,2,0,4,1,8,0,6,4,1,9,2,7,5,1,2,0,3,0,3,5,1,
%U A047787 7,0,7,5,7,1,6,8,7,5,5,0,6,3,0,8,9,4,3,3,1,8,9,6,1,8,3,7,4,9,6,7,1,2,4,6,9
%N A047787 Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function.
%C A047787 Decimal expansion of -psi(1/3). - _Benoit Cloitre_, Mar 07 2004
%D A047787 S. J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135
%H A047787 G. C. Greubel, <a href="/A047787/b047787.txt">Table of n, a(n) for n = 1..10000</a>
%H A047787 <a href="/index/Di#differential_equations">Index entries for sequences related to the digamma function</a>
%F A047787 Gamma'(1/3)/Gamma(1/3)=-EulerGamma-(3/2)*log(3)-Pi/(2*sqrt(3))=-3.13203378002... where EulerGamma is the Euler-Mascheroni constant (A001620).
%e A047787 3.1320337...
%t A047787 RealDigits[PolyGamma[1/3], 10, 105] // First (* _Jean-François Alcover_, Aug 08 2015 *)
%o A047787 (PARI) Euler+(3/2)*log(3)+Pi/(2*sqrt(3))
%o A047787 (Magma) SetDefaultRealField(RealField(100)); R:= RealField();
%o A047787 EulerGamma(R) + (3/2)*Log(3) + Pi(R)/(2*Sqrt(3)); // _G. C. Greubel_, Aug 28 2018
%K A047787 cons,nonn
%O A047787 1,1
%A A047787 _Benoit Cloitre_, May 24 2003