A263498 Decimal expansion of the Gaussian Hypergeometric Function 2F1(1, 3; 5/2; x) at x=1/4.

1, 4, 1, 8, 3, 9, 9, 1, 5, 2, 3, 1, 2, 2, 9, 0, 4, 6, 7, 4, 5, 8, 7, 7, 1, 0, 1, 0, 1, 8, 9, 5, 4, 0, 9, 7, 6, 3, 7, 8, 7, 5, 4, 9, 9, 7, 4, 5, 6, 9, 8, 7, 4, 3, 4, 0, 9, 3, 1, 7, 9, 9, 1, 3, 8, 5, 0, 8, 3, 0, 9, 0, 8, 1, 6, 8, 4, 7, 1, 8, 4, 4, 9, 1, 2, 1, 6, 6, 6, 5, 0, 9, 4, 9, 4, 1

Offset: 1

Author

R. J. Mathar, Oct 19 2015

Keywords

• cons
• nonn

Comments

Division through 3 gives 0.472799.. = integral_{x=0..infinity} x^2*I_1(x)*K_1(x)^2 dx, where I and K are Modified Bessel Functions.

Examples

			1.41839915231229046745877101018954097637875499745698743409317991385...
		

Crossrefs

Cf. A073010.

Programs

Mathematica

RealDigits[4*Pi/3^(3/2) - 1, 10, 120][[1]] (* Vaclav Kotesovec, Apr 10 2016 *)

PARI

4*Pi/sqrt(27)-1 \\ Charles R Greathouse IV, Aug 01 2016

Formula

Equals 4*Pi/3^(3/2) - 1. - Vaclav Kotesovec, Apr 10 2016