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A137274 Even terms in the Taylor series for the Fisher Information of a Rice-distributed variable (at amplitude 0, with sigma==1). 0

%I #6 Oct 09 2023 05:26:52

%S 0,2,-24,900,-80640,14288400,-4400827200,2156641086600,

%T -1577763611424000,1642267210487904000,-2342289079736686080000,

%U 4440975210468688551660000,-10917777323646285908175360000,34083310964641049282713542000000,-132737301192061195797209453611200000

%N Even terms in the Taylor series for the Fisher Information of a Rice-distributed variable (at amplitude 0, with sigma==1).

%C The odd terms of this Taylor expansion are zero.

%F 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}]

%t 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 *)

%K sign

%O 0,2

%A D. H. J. Poot (dirk.poot(AT)ua.ac.be), Mar 13 2008

%E More terms from _Vaclav Kotesovec_, Oct 09 2023

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Last modified May 26 22:32 EDT 2024. Contains 372847 sequences. (Running on oeis4.)