cp's OEIS Frontend

A105372 Decimal expansion of Hypergeometric2F1[ -(1/4),3/4,1,1] = sqrt(Pi)/(Gamma[1/4]*Gamma[5/4]).

%I A105372 #25 Aug 26 2020 02:55:37
%S A105372 5,3,9,3,5,2,6,0,1,1,8,8,3,7,9,3,5,6,6,6,7,9,3,5,7,2,2,3,5,5,5,5,2,7,
%T A105372 3,2,7,6,5,8,6,8,9,6,5,4,4,3,0,4,0,1,3,0,3,3,9,9,4,6,6,3,1,8,6,3,8,8,
%U A105372 2,9,8,8,4,8,6,5,1,5,6,8,2,8,1,5,5,9,2,1,3,7,2,2,7,5,3,3,7,7,1,4
%N A105372 Decimal expansion of Hypergeometric2F1[ -(1/4),3/4,1,1] = sqrt(Pi)/(Gamma[1/4]*Gamma[5/4]).
%C A105372 This constant appears in solution to an ODE considered in A104996, A104997.
%H A105372 G. C. Greubel, <a href="/A105372/b105372.txt">Table of n, a(n) for n = 0..5000</a>
%H A105372 Andrei Gruzinov, <a href="https://doi.org/10.1103/PhysRevLett.94.021101">Power of an axisymmetric pulsar</a>, Physical Review Letters, Vol. 94, No. 2 (2005), 021101, <a href="https://arxiv.org/abs/astro-ph/0407279">preprint</a>, arXiv:astro-ph/0407279, 2004.
%F A105372 Hypergeometric2F1[ -(1/4), 3/4, 1, 1] = Sqrt[Pi]/(Gamma[1/4]*Gamma[5/4]).
%F A105372 From _Vaclav Kotesovec_, Jun 15 2015: (Start)
%F A105372 4*sqrt(Pi)/Gamma(1/4)^2.
%F A105372 1 / EllipticK(1/sqrt(2)) (Maple notation).
%F A105372 1 / EllipticK[1/2] (Mathematica notation).
%F A105372 (End)
%F A105372 Equals Product_{k>=1} (1 + (-1)^k/(2*k)). - _Amiram Eldar_, Aug 26 2020
%e A105372 0.53935260118837935666793572235555273276586896544304013033994...
%p A105372 evalf(1/EllipticK(1/sqrt(2)),120); # _Vaclav Kotesovec_, Jun 15 2015
%t A105372 RealDigits[1/EllipticK[1/2],10,120][[1]] (* _Vaclav Kotesovec_, Jun 15 2015 *)
%o A105372 (PARI) sqrt(Pi)/(gamma(1/4)*gamma(5/4)) \\ _G. C. Greubel_, Jan 09 2017
%Y A105372 Cf. A093341, A104996, A104997.
%K A105372 cons,nonn
%O A105372 0,1
%A A105372 _Zak Seidov_, Apr 02 2005
%E A105372 Last digit corrected by _Vaclav Kotesovec_, Jun 15 2015