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

Author

Jean-François Alcover, Jul 10 2014

Keywords

• nonn
• cons
• walk

Examples

			2.1422044985256634680139197847019650201206458017918000691935563806464998832...
		

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

Crossrefs

Cf. A244996.

Programs

Mathematica

Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; RealDigits[2 + (3/Pi)*Clausen2[Pi/3] - 3*Sqrt[3]/(2*Pi), 10, 105] // First

PARI

2 + 3*imag(polylog(2, exp(Pi*I/3)))/Pi - 3*sqrt(3)/2/Pi \\ Charles R Greathouse IV, Aug 27 2014

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).