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  • $\begingroup$ Why not evaluate the integral directly? $\endgroup$ Commented Feb 26, 2015 at 12:02
  • $\begingroup$ Because $f(y)$ is an arbitrary function. $\endgroup$ Commented Feb 26, 2015 at 12:03
  • $\begingroup$ (at) Julian: See my solution, which assumes that f[x] can be expanded into a power series. $\endgroup$ Commented Feb 26, 2015 at 12:45
  • $\begingroup$ Because you have replaced σ by ρ in the integrand, I think you should expand in ρ, not σ, which now is just a coefficient in the definition of z that has no connection to ρ. More generally, it seems to me that you would do better to move this question to Mathematics.SE. The issue is how to transform the integrand into a form that can be expanded in ρ, which is not a Mathematica.SE question. Once that is solved, doing the expansion with Mathematica should be straightforward. $\endgroup$ Commented Feb 26, 2015 at 15:43
  • $\begingroup$ Apologies, I forgot to define $\rho=\sigma\sqrt{y}$ which is now corrected. $\endgroup$ Commented Feb 26, 2015 at 15:49