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A145962 Decimal expansion of (1/5)*Hypergeometric2F1[1, 5/8, 13/8, 1/16] used in BBP Pi formula.

%I A145962 #24 Feb 16 2025 08:33:09
%S A145962 2,0,5,0,0,2,5,5,7,6,3,6,4,2,3,5,3,3,9,4,4,1,5,0,3,3,6,2,1,8,4,9,2,2,
%T A145962 6,6,9,0,6,1,6,5,2,4,2,7,1,2,1,4,9,4,3,9,6,0,0,0,1,8,5,0,6,3,4,7,8,0,
%U A145962 9,8,9,5,8,6,1,2,0,9,3,0,1,4,5,4,5,0,7,6,4,1,6,9,2,8,2,2,9,0,3,3
%N A145962 Decimal expansion of (1/5)*Hypergeometric2F1[1, 5/8, 13/8, 1/16] used in BBP Pi formula.
%C A145962 BBP formula for Pi = 4*A145963 - (1/2)*A145960 - (1/2)*A145961 - A145962.
%H A145962 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BBPFormula.html">BBP Formula</a>
%F A145962 Equals Sum_{k>=0} (1/16)^k / (8*k+5).
%e A145962 0.2050025576364235339441503362184922669061652427121494396000185063478...
%t A145962 RealDigits[1/5 Hypergeometric2F1[1, 5/8, 13/8, 1/16], 10, 100][[1]]
%t A145962 N[Sum[(1/16)^n (1/(8n+5)),{n,0,Infinity}], 100]
%t A145962 N[Sqrt[2](ArcCot[Sqrt[2]] + ArcCoth[Sqrt[2]]) -Pi/4 - ArcCot[3] - Log[5]/2, 100]
%o A145962 (PARI) suminf(k=0, (1/16)^k / (8*k+5)) \\ _Michel Marcus_, Jan 16 2021
%Y A145962 Cf. A000796, A145960, A145961, A145963.
%K A145962 cons,nonn
%O A145962 0,1
%A A145962 _Artur Jasinski_, Oct 25 2008
%E A145962 Leading zero removed, offset adjusted by _R. J. Mathar_, Feb 05 2009