kstephe6
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(the following is Mathematica code)
For the rice pdf...
P(x)=(x/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)]
...the Second raw moment is given by doing the integral...
Integrate[(x^3/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)], {x, 0, Infinity}]
While the answer is known to be...
2 σ^2 + ν^2
...I have no idea how to arrive at this answer by hand (ie without using Mathematica). I am currently doing a little research for grins and giggles on a very closely related integral, and knowing how to solve the one above would be of great use to me. Any help in this endeavor... Even suggestions as to where I might find the derivation... would be greatly appreciated.
For the rice pdf...
P(x)=(x/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)]
...the Second raw moment is given by doing the integral...
Integrate[(x^3/σ^2) BesselI[0, x (ν/σ^2)] Exp[-(x^2 + ν^2)/(2 σ^2)], {x, 0, Infinity}]
While the answer is known to be...
2 σ^2 + ν^2
...I have no idea how to arrive at this answer by hand (ie without using Mathematica). I am currently doing a little research for grins and giggles on a very closely related integral, and knowing how to solve the one above would be of great use to me. Any help in this endeavor... Even suggestions as to where I might find the derivation... would be greatly appreciated.