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A245025
Decimal expansion of the moment derivative W_3'(2) associated with the radial probability distribution of a 3-step uniform random walk.
2
2, 1, 4, 2, 2, 0, 4, 4, 9, 8, 5, 2, 5, 6, 6, 3, 4, 6, 8, 0, 1, 3, 9, 1, 9, 7, 8, 4, 7, 0, 1, 9, 6, 5, 0, 2, 0, 1, 2, 0, 6, 4, 5, 8, 0, 1, 7, 9, 1, 8, 0, 0, 0, 6, 9, 1, 9, 3, 5, 5, 6, 3, 8, 0, 6, 4, 6, 4, 9, 9, 8, 8, 3, 2, 1, 7, 9, 0, 4, 8, 3, 3, 9, 9, 0, 7, 9, 2, 7, 8, 4, 0, 3, 3, 3, 5, 7, 8, 4, 2, 4, 0, 8, 9, 1
OFFSET
1,1
LINKS
Jonathan M. Borwein, Armin Straub, James Wan, and Wadim Zudilin, Densities of Short Uniform Random Walks p. 978, Canad. J. Math. 64(2012), 961-990.
Eric Weisstein's MathWorld, Clausen's Integral
FORMULA
W_3'(2) = 2 + (3/Pi)*Cl2(Pi/3) - 3*sqrt(3)/(2*Pi), where Cl2 is the Clausen function.
W_3'(2) = 2 + 3*W_3'(0) - 3*sqrt(3)/(2*Pi).
EXAMPLE
2.1422044985256634680139197847019650201206458017918000691935563806464998832...
MATHEMATICA
Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; RealDigits[2 + (3/Pi)*Clausen2[Pi/3] - 3*Sqrt[3]/(2*Pi), 10, 105] // First
PROG
(PARI) 2 + 3*imag(polylog(2, exp(Pi*I/3)))/Pi - 3*sqrt(3)/2/Pi \\ Charles R Greathouse IV, Aug 27 2014
CROSSREFS
Cf. A244996.
Sequence in context: A239101 A362266 A145983 * A257495 A120025 A109090
KEYWORD
nonn,cons,walk
AUTHOR
STATUS
approved