A376009 Decimal expansion of the hypergeometric series 3F2(3/4,5/4,1; 2,2 ;1).

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

Offset

1,2

Links

Table of n, a(n) for n=1..87.

W. N. Bailey, Contiguous hypergeometric functions of the type 3F2, Proc. Glasg. Math. Ass. 2 (1954) 62-65.

James D. Evans, Evaluation of four irrational definite sine integrals using residue theory, Appl. Math. Comp 36 (1990) 163-172, eq. (16).

Formula

(1/8)* this = 2 -(15/16) * 2F1(3/4,5/4 ; 3 ;1). [Bailey eq (4.5)]

Integral_(x= 0.. 2*Pi) sqrt(1+sin x) dx = 5.6569... = 2*Pi*(1-this /16). [Evans N_1]

Equals 16 - 32*sqrt(2)/Pi. - Amiram Eldar, Sep 06 2024

Example

1.59493894148...

Maple

16-15/2*hypergeom([3/4, 5/4], [3], 1) ; evalf(%) ;

Mathematica

RealDigits[16 - 32*Sqrt[2]/Pi, 10, 120][[1]] (* Amiram Eldar, Sep 06 2024 *)

Crossrefs

Sequence in context: A196754 A198217 A021631 * A201325 A372285 A359485

Adjacent sequences: A376006 A376007 A376008 * A376010 A376011 A376012

Keyword

cons,nonn

Author

R. J. Mathar, Sep 05 2024

Status

approved