A245025 Decimal expansion of the moment derivative W_3'(2) associated with the radial probability distribution of a 3-step uniform random walk.

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

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: A239101 A362266 A145983 * A257495 A120025 A109090

Adjacent sequences: A245022 A245023 A245024 * A245026 A245027 A245028

Keyword

nonn,cons,walk

Author

Jean-François Alcover, Jul 10 2014

Status

approved