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A102521 Decimal expansion of value of Ahmed's 2nd integral.

%I A102521 #15 Feb 16 2025 08:32:56
%S A102521 5,9,0,4,8,9,2,7,0,8,8,6,3,8,5,0,7,5,1,5,9,2,9,8,1,3,9,5,7,1,5,6,8,4,
%T A102521 6,3,5,4,6,5,1,3,3,6,1,3,5,5,6,3,9,3,4,8,8,6,1,9,0,6,8,8,8,8,2,6,6,5,
%U A102521 8,2,2,0,4,4,8,8,6,1,8,0,2,0,2,9,3,6,0,0,9,5,5,9,5,2,2,5,4,3,5,3,4,1
%N A102521 Decimal expansion of value of Ahmed's 2nd integral.
%D A102521 Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.
%H A102521 G. C. Greubel, <a href="/A102521/b102521.txt">Table of n, a(n) for n = 1..5000</a>
%H A102521 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AhmedsIntegral.html">Ahmed's Integral</a>
%F A102521 Equals Pi/4 - Pi/sqrt(2) + (3*arctan(sqrt(2)))/sqrt(2).
%F A102521 Equals Integral_{x=0..1} arctan(sqrt(x^2 + 1))/(x^2 + 1)^(3/2) dx (Borwein et al., 2004). - _Amiram Eldar_, Aug 17 2020
%e A102521 0.590489270886385075159298139571568463546513361355639...
%t A102521 RealDigits[Pi/4 - Pi/Sqrt[2] + (3*ArcTan[Sqrt[2]])/Sqrt[2], 10, 50][[1]] (* _G. C. Greubel_, Jun 02 2017 *)
%o A102521 (PARI) Pi/4 - Pi/sqrt(2) + (3*atan(sqrt(2)))/sqrt(2) \\ _G. C. Greubel_, Jun 02 2017
%Y A102521 Cf. A096615, A098459.
%K A102521 nonn,cons
%O A102521 1,1
%A A102521 _Eric W. Weisstein_, Jan 14 2005