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

%I

%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="http://moodle.thecarma.net/jon/ontology.pdf">Experimental computation as an ontological game changer, 2014.</a> p. 14. [broken link]

%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

%O 0,1

%A _Jean-Fran├žois Alcover_, Jul 07 2014

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)