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A293237
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Decimal expansion of the escape probability for a random walk on the 3D fcc lattice.
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3
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7, 4, 3, 6, 8, 1, 7, 6, 3, 4, 9, 5, 3, 5, 1, 2, 2, 8, 9, 0, 4, 9, 6, 9, 8, 1, 9, 3, 6, 5, 3, 7, 6, 4, 8, 0, 5, 0, 9, 6, 0, 2, 2, 5, 0, 9, 0, 5, 1, 2, 1, 7, 0, 5, 6, 6, 2, 0, 4, 4, 3, 9, 3, 4, 0, 1, 9, 4, 3, 3, 5, 6, 7, 3, 5, 3, 7, 6, 6, 8, 2, 2, 9, 6, 1, 1, 0
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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.
The escape probability for the hcp lattice also equals this constant. The escape probability for the diamond lattice is 3/4 times this constant.
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LINKS
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FORMULA
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Equals 2^(14/3)*Pi^4/(9*Gamma(1/3)^6).
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EXAMPLE
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0.74368176349535122890496981936537648...
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MATHEMATICA
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RealDigits[2^(14/3)*Pi^4/(9*Gamma[1/3]^6), 10, 100][[1]] (* G. C. Greubel, Oct 26 2018 *)
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PROG
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(PARI) 2^(14/3)*Pi^4/(9*gamma(1/3)^6) \\ Altug Alkan, Apr 09 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2^(14/3)*Pi(R)^4/(9*Gamma(1/3)^6); // 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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