OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Andrei Gruzinov, Power of an axisymmetric pulsar, Physical Review Letters, Vol. 94, No. 2 (2005), 021101, preprint, arXiv:astro-ph/0407279, 2004.
FORMULA
Hypergeometric2F1[ -(1/4), 3/4, 1, 1] = Sqrt[Pi]/(Gamma[1/4]*Gamma[5/4]).
From Vaclav Kotesovec, Jun 15 2015: (Start)
4*sqrt(Pi)/Gamma(1/4)^2.
1 / EllipticK(1/sqrt(2)) (Maple notation).
1 / EllipticK[1/2] (Mathematica notation).
(End)
Equals Product_{k>=1} (1 + (-1)^k/(2*k)). - Amiram Eldar, Aug 26 2020
EXAMPLE
0.53935260118837935666793572235555273276586896544304013033994...
MAPLE
evalf(1/EllipticK(1/sqrt(2)), 120); # Vaclav Kotesovec, Jun 15 2015
MATHEMATICA
RealDigits[1/EllipticK[1/2], 10, 120][[1]] (* Vaclav Kotesovec, Jun 15 2015 *)
PROG
(PARI) sqrt(Pi)/(gamma(1/4)*gamma(5/4)) \\ G. C. Greubel, Jan 09 2017
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Zak Seidov, Apr 02 2005
EXTENSIONS
Last digit corrected by Vaclav Kotesovec, Jun 15 2015
STATUS
approved