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A273951 Decimal expansion the even Bessel moment s(4,0) = Integral_{0..inf} I_0(x) K_0(x)^3 dx. 0

%I

%S 6,9,9,7,5,6,3,0,1,6,6,8,0,6,3,2,3,5,9,5,5,6,7,5,7,8,2,6,8,5,3,0,9,6,

%T 0,0,5,6,9,7,7,5,4,2,8,4,3,5,3,3,6,2,9,0,8,3,3,6,2,5,5,8,0,7,2,7,1,3,

%U 6,8,8,6,2,5,3,8,5,8,4,4,1,9,9,4,0,1,1,7,0,9,2,8,9,6,5,2,8,7,8,6,9,3,3

%N Decimal expansion the even Bessel moment s(4,0) = Integral_{0..inf} I_0(x) K_0(x)^3 dx.

%H David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, <a href="http://arxiv.org/abs/0801.0891">Elliptic integral evaluations of Bessel moments</a>, arXiv:0801.0891, page 19.

%F s(4,0) = Integral_{0..Pi/4) 4 EllipticK(-tan(x)^2) EllipticK(-cot(x)^2) / sin(2x) dx, where EllipticK is the complete elliptic integral of the first kind.

%F N.B. K(k) used in the paper is related to Mathematica's EllipticK(k) by K(k) = EllipticK(k^2/(k^2-1))/sqrt(1 - k^2).

%e 6.997563016680632359556757826853096005697754284353362908336255807...

%t s[4, 0] = NIntegrate[4 EllipticK[-Cot[t]^2] EllipticK[-Tan[t]^2] /Sin[2 t], {t, 0, Pi/4}, WorkingPrecision -> 103];

%t RealDigits[s[4, 0]][[1]]

%Y Cf. A222068 (odd moment s(4,1)).

%K nonn,cons

%O 1,1

%A _Jean-Fran├žois Alcover_, Jun 05 2016

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Last modified August 4 13:38 EDT 2020. Contains 336201 sequences. (Running on oeis4.)