Dear all,
I would like to ask if anyone of you knows where to get the Laplace transform of the following function:
f(t) = I_n(a*t) * J_m(b*sqrt{t})
With
I_n() = Modified Bessel function of the first kind, of integer order n
J_m() = Bessel function of the first kind, of integer order m
a,b = real numbers
I was trying to look up in the book
A.P. Prudnikov, "Integrals and series, vol. 4 Laplace transforms"
but is not available in my library until march 8th!
I thank your kind help,
Home-made-bread.
Hello everybody,
I first thank CaptainBlack so much for answering, I even did not know about Library Genesis. I think I will use it a lot in the future!
However, Prudnikov's book does not give the result I am looking for. Any other suggestion?
Thanks in advance.
My best regards, Home-made-bread
Yeah, numerically. Ok, suppose I wanted to know what the Laplace Transform of that was at then I'd do the following in Mathematia:
Bingo. Then I claim:Code:In[3]:= n = 2; m = 3; a = 1; b = 1/2; s = 2; NIntegrate[ BesselI[n, a t] BesselJ[m, b Sqrt[t]] Exp[-s t], {t, 0, \[Infinity]}] Out[8]= 0.000288939
and if I needed to, I could do this for any values of the parameters and as long as the integration is well-behaved, I could obtain the value of the transform pretty accurately and if necessary, run a fit on the data points to obtain a least-square fit function even if were complex.