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I am doing a Schwarz-Christoffel transformation and I am trying to calculate the integral analytically using the residue theorem.

My integral is the following:

[tex]\int^\zeta _{\zeta_0} (z+1)\frac{1}{(z+2.9)^{{b_1}/\pi}{(z-0.5)^{{b_2}/\pi}}}dz[/tex]

This has two poles at -2.9 and 0.5. [itex]b_1[/itex] and [itex]b_2[/itex] are not integers.

I want to do this integral for a contour that contains both poles. I know how to use the Laurent series to extract the [itex]a_{-1}[/itex] term (residue) needed for the residue theorem for integer powers (which is to take the limit of the derivative of the same power). Does anyone know how I can find the residue for a function where the poles are raised to a non-integer power?

Cheers

P.S. Lately my fraction lines appear in the web browser distorted, anyone knows what's up with that??