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

%I #18 Feb 27 2022 13:14:53

%S 1,1,3,12,60,355,2380,17430,134190,1027656,6922146,21248073,

%T -601744143,-20802115620,-480211746300,-9737801866650,

%U -183103121602830,-3185750996194910,-48580593174777092,-515943195216679230,3196232280583478136,460669417734237239892

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

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

%H Noam D. Elkies, Reply to <a href="https://mathoverflow.net/questions/83317/polyas-random-walk-constants-at-infinity">Pólya’s Random Walk Constants at infinity</a>, MathOverflow Q-83317, Dec 13 2011.

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

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

%K sign

%O 0,3

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

%E Terms a(9) and beyond from _Andrey Zabolotskiy_, Feb 27 2022