Is it possible to use the Euler-Maclaurin Formula to approximate complex valued line integrals?

Question

I was wondering if it is sometimes possible to use the Euler-Maclaurin Formula to approximate line integrals in the complex plane?

Answer 1

Yes. Assuming the curve C over which you're integrating is continuously differentiable, the line integral of f over C can be described as an integral of a function of a real variable:

integral of f over C = integral from a to b of f(g(t))g'(t) dt

so now apply the formula to the real and imaginary parts of the integrand, separately.

Answer 2

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