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A293238
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Decimal expansion of the escape probability for a random walk on the 3D bcc lattice.
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5
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7, 1, 7, 7, 7, 0, 0, 1, 1, 0, 4, 6, 1, 2, 9, 9, 9, 7, 8, 2, 1, 1, 9, 3, 2, 2, 3, 6, 6, 5, 7, 7, 9, 4, 2, 6, 6, 5, 7, 1, 2, 9, 8, 8, 9, 3, 3, 9, 9, 8, 4, 3, 7, 1, 9, 8, 9, 7, 6, 3, 6, 6, 3, 8, 7, 7, 2, 6, 9, 4, 2, 3, 1, 2, 5, 8, 4, 9, 8, 6, 6, 3, 7, 0, 1, 6, 1
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OFFSET
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0,1
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COMMENTS
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The return probability equals unity minus this constant. The expected number of visits to the origin is the inverse of this constant, A091670.
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LINKS
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FORMULA
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Pi^2/(4*K(1/sqrt(2))^2), where K is the complete elliptic integral of the first kind.
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EXAMPLE
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0.7177700110461299978211932236657794...
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MATHEMATICA
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RealDigits[(4*Pi^3)/Gamma[1/4]^4, 10, 100][[1]] (* G. C. Greubel, Oct 26 2018 *)
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PROG
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(PARI) default(realprecision, 100); (4*Pi^3)/gamma(1/4)^4 \\ G. C. Greubel, Oct 26 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (4*Pi(R)^3)/Gamma(1/4)^4; // G. C. Greubel, Oct 26 2018
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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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