OFFSET
0,2
COMMENTS
The odd terms of this Taylor expansion are zero.
FORMULA
Integrate[ D[ x*exp( -(A^2 + x^2)/2 ) * BesselI[0,A*x] * (A-x*BesselI[1,A*x]/BesselI[0,A*x])^2, {A,2*k}], {x,0,\[Infinity]},Assumptions -> {A == 0}]
MATHEMATICA
nmax = 10; Table[(CoefficientList[Integrate[Series[x*E^(-(A^2 + x^2)/2) * BesselI[0, A*x]*(A - x*BesselI[1, A*x]/BesselI[0, A*x])^2, {A, 0, 2*nmax}], {x, 0, Infinity}], A] * Range[0, 2*nmax]!)[[2*k + 1]], {k, 0, nmax}] (* Vaclav Kotesovec, Oct 09 2023 *)
CROSSREFS
KEYWORD
sign
AUTHOR
D. H. J. Poot (dirk.poot(AT)ua.ac.be), Mar 13 2008
EXTENSIONS
More terms from Vaclav Kotesovec, Oct 09 2023
STATUS
approved