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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

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: A127136 A239101 A145983 * A257495 A120025 A109090

Adjacent sequences:  A245022 A245023 A245024 * A245026 A245027 A245028

KEYWORD

nonn,cons,walk

AUTHOR

Jean-Fran├žois Alcover, Jul 10 2014

STATUS

approved

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)