

A273951


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


0



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, 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, 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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..103.
David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891, page 19.


FORMULA

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.
N.B. K(k) used in the paper is related to Mathematica's EllipticK(k) by K(k) = EllipticK(k^2/(k^21))/sqrt(1  k^2).


EXAMPLE

6.997563016680632359556757826853096005697754284353362908336255807...


MATHEMATICA

s[4, 0] = NIntegrate[4 EllipticK[Cot[t]^2] EllipticK[Tan[t]^2] /Sin[2 t], {t, 0, Pi/4}, WorkingPrecision > 103];
RealDigits[s[4, 0]][[1]]


CROSSREFS

Cf. A222068 (odd moment s(4,1)).
Sequence in context: A246709 A051496 A195296 * A307053 A100403 A066002
Adjacent sequences: A273948 A273949 A273950 * A273952 A273953 A273954


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Jun 05 2016


STATUS

approved



