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A248080
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Decimal expansion of P_0(xi), the maximum limiting probability that a random n-permutation has no cycle exceeding a given length.
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1
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0, 9, 8, 7, 1, 1, 7, 5, 4, 4, 8, 0, 7, 1, 4, 6, 9, 2, 4, 9, 3, 7, 2, 1, 3, 0, 8, 2, 3, 7, 0, 2, 0, 6, 7, 9, 9, 3, 3, 3, 3, 3, 3, 5, 4, 7, 8, 0, 8, 4, 4, 0, 0, 0, 2, 5, 6, 6, 9, 7, 9, 0, 8, 3, 6, 2, 2, 5, 2, 5, 3, 6, 4, 2, 7, 4, 0, 6, 3, 0, 1, 5, 8, 6, 2, 6, 3, 0, 0, 2, 1, 5, 7, 5, 9, 2, 4, 5, 4, 6, 1, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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(1/2)*log(1 + sqrt(e))^2 - log(1 + sqrt(e)) + Li_2(1/(1 + sqrt(e))) - Pi^2/12 + 1.
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EXAMPLE
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0.098711754480714692493721308237020679933333354780844...
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MATHEMATICA
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xi = 1/(1 + Sqrt[E]); P0[x_] := Log[x]^2/2 + Log[x] + PolyLog[2, x] - Pi^2/12 + 1; Join[{0}, RealDigits[P0[xi], 10, 101] // First]
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PROG
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(Python)
from mpmath import *
mp.dps=102
xi=1/(1 + sqrt(e))
C = log(xi)**2/2 + log(xi) + polylog(2, xi) - pi**2/12 + 1
print([int(n) for n in list(str(C)[2:-1])]) # Indranil Ghosh, Jul 04 2017
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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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