A244844 Decimal expansion of 2F1(1, 1/4; 5/4; -1/4), where 2F1 is a Gaussian hypergeometric function.

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

Offset

0,1

Comments

This constant is mentioned by Bailey & Borwein as an example of the use of the PSLQ integer relation algorithm to discover new formulas.

Links

Table of n, a(n) for n=0..103.

D. H. Bailey and J. M. Borwein, Experimental computation as an ontological game changer, 2014, p. 14.

Eric Weisstein's MathWorld, Hypergeometric Function.

Eric Weisstein's MathWorld, PSLQ Algorithm.

Formula

4*2F1(1, 1/4; 5/4; -1/4) + 2*arctan(1/2) - log(5) = Pi.

Example

0.9559338370055703451587225633958154299164241612678457538164315765853999...

Mathematica

Hypergeometric2F1[1, 1/4, 5/4, -1/4] // RealDigits[#, 10, 104]& // First

Crossrefs

Sequence in context: A154683 A200026 A262276 * A255896 A346011 A019882

Adjacent sequences: A244841 A244842 A244843 * A244845 A244846 A244847

Keyword

cons,nonn

Author

Jean-François Alcover, Jul 07 2014

Status

approved