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%I #16 Apr 05 2024 11:07:04
%S 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,
%T 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,
%U 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
%N Decimal expansion of 2F1(1, 1/4; 5/4; -1/4), where 2F1 is a Gaussian hypergeometric function.
%C This constant is mentioned by Bailey & Borwein as an example of the use of the PSLQ integer relation algorithm to discover new formulas.
%H D. H. Bailey and J. M. Borwein, <a href="https://www.carmamaths.org/resources/jon/ontology.pdf">Experimental computation as an ontological game changer</a>, 2014, p. 14.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/HypergeometricFunction.html">Hypergeometric Function</a>.
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PSLQAlgorithm.html">PSLQ Algorithm</a>.
%F 4*2F1(1, 1/4; 5/4; -1/4) + 2*arctan(1/2) - log(5) = Pi.
%e 0.9559338370055703451587225633958154299164241612678457538164315765853999...
%t Hypergeometric2F1[1, 1/4, 5/4, -1/4] // RealDigits[#, 10, 104]& // First
%K cons,nonn,changed
%O 0,1
%A _Jean-François Alcover_, Jul 07 2014
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