I want to program an integration routine in C++ using the GSL library but for complex functions.How should I split my integrand to apply the gsl_integration_qag function on it.Just integrate the real and imaginary parts by themselves is not correct I guess.I have the following function:$$S(a,N) = S(a, \infty) - \sum^{\infty}_{n = 1} \frac{1}{n + N}$$where $S(a, \infty)$ is some real constant.The functions I later intend to integrate are using the harmonic sum as a basis but are just sums of it.The integration I intend to do is the Mellin transform which is given by:$$f(x) = \frac{1}{2 \pi i} \int_C dn x^{-n} f^{M}(n).$$Any help is much approciated.EDIT: Any idea on a C++ program for complex numerical integration?
Complex Numerical Integration using GSL
c++;integration;complex analysis