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

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, 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, 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

Offset: 0

Author

Zak Seidov, Apr 02 2005

Keywords

• cons
• nonn

Comments

This constant appears in solution to an ODE considered in A104996, A104997.

Examples

			0.53935260118837935666793572235555273276586896544304013033994...
		

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.

Crossrefs

Cf. A093341, A104996, A104997.

Programs

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 *)

PARI

sqrt(Pi)/(gamma(1/4)*gamma(5/4)) \\ G. C. Greubel, Jan 09 2017

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

Extensions

Last digit corrected by Vaclav Kotesovec, Jun 15 2015