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

0, 2, -24, 900, -80640, 14288400, -4400827200, 2156641086600, -1577763611424000, 1642267210487904000, -2342289079736686080000, 4440975210468688551660000, -10917777323646285908175360000, 34083310964641049282713542000000, -132737301192061195797209453611200000

Offset

0,2

Comments

The odd terms of this Taylor expansion are zero.

Links

Table of n, a(n) for n=0..14.

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

Sequence in context: A264559 A012186 A012081 * A002032 A015212 A012228

Adjacent sequences: A137271 A137272 A137273 * A137275 A137276 A137277

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