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A273951
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Decimal expansion the even Bessel moment s(4,0) = Integral_{0..inf} I_0(x) K_0(x)^3 dx.
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0
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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
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1,1
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LINKS
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FORMULA
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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^2-1))/sqrt(1 - k^2).
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EXAMPLE
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6.997563016680632359556757826853096005697754284353362908336255807...
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MATHEMATICA
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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]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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