Hi all!

I am trying to compute improper integrals as a function of additional parameters, where the integrand contains a special function, e.g.:

$\displaystyle f(a,t) := \int_0^{\infty}e^{-aq^2}S(a,q,t)dq$

where S(a,q,t) is the Mathieu sine (solution to Mathieu's ODE), cf:

Mathieu function - Wikipedia, the free encyclopedia

This special function is implemented in Mathematica underI am interested in the (approximate) dependence of the above improper integral on the parameters a and t. Since the integration is not possible analytically, I tried to do it numerically usingMathieuS[a, q, t]but got an error, since I use parameters in the integrand and not numbers.NIntegrate

Is there any way of getting the a and/or t dependence of such a function numerically? Taylor or Fourier expansions of them /to an arbitrary order/ are absolutely sufficient

With regards,

marin