A105227 Coefficients of the expansion in 1/(2d) of the Green function G(0,1) for brownian motion.

1, 1, 3, 12, 60, 355, 2380, 17430, 134190, 1027656, 6922146, 21248073, -601744143, -20802115620, -480211746300, -9737801866650, -183103121602830, -3185750996194910, -48580593174777092, -515943195216679230, 3196232280583478136, 460669417734237239892

Offset

0,3

References

C. Itzykson and J.-M. Drouffe, Statistical Field Theory, 1989.

Links

Table of n, a(n) for n=0..21.

Noam D. Elkies, Reply to Pólya’s Random Walk Constants at infinity, MathOverflow Q-83317, Dec 13 2011.

Formula

G.f.: Integral_{t=0..oo} BesselI(0,2*t*x)^(1/(2*x))*exp(-t) dt. - Alois P. Heinz, Feb 27 2022

Mathematica

CoefficientList[Integrate[BesselI[0, 2 t x]^(1/(2 x)) Exp[-t] + O[x]^20, {t, 0, Infinity}], x] (* Andrey Zabolotskiy, Feb 27 2022 *)

Crossrefs

Sequence in context: A020052 A096471 A140097 * A370652 A000258 A326242

Adjacent sequences: A105224 A105225 A105226 * A105228 A105229 A105230

Keyword

sign

Author

Michele Dondi (blazar(AT)lcm.mi.infn.it), Apr 14 2005

Extensions

Terms a(9) and beyond from Andrey Zabolotskiy, Feb 27 2022

Status

approved