A263490 Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2 ; 1,1; x) at x=1/4.

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

Offset: 1

Author

R. J. Mathar, Oct 19 2015

Keywords

• cons
• nonn

Comments

Multiplication with Pi^2/4 gives 2.554057.. = integral_{x=0..infinity} I_0(x) *K_0(x)^2 dx, where I and K are Modified Bessel Functions.

Examples

			1.0351206614256489810459575514...
		

Programs

Maple

evalf(4*EllipticK(sqrt(2-sqrt(3))/2)^2 / Pi^2, 120); # Vaclav Kotesovec, Apr 10 2016

Mathematica

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

PARI

4*ellK(sqrt(2-sqrt(3))/2)^2/Pi^2 \\ Charles R Greathouse IV, Feb 04 2025

Formula

Square of A243308.

From Vaclav Kotesovec, Apr 10 2016: (Start)

Equals 3^(1/2) * Gamma(1/3)^6 / (2^(8/3) * Pi^4).

Equals Gamma(1/6)^3 / (3 * 2^(5/3) * Pi^(5/2)).

(End)