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

Author

Jean-François Alcover, Jul 07 2014

Keywords

• cons
• nonn

Comments

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

Examples

			0.9559338370055703451587225633958154299164241612678457538164315765853999...
		

Links

• 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.

Programs

Mathematica

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

Formula

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