This is basically a follow-up question to "Evaluate $\oint \exp\Big(\frac{A}{x-1}\Big) \cdot \exp\Big(\frac{B}{x-2}\Big) dx$ - Integral with two essential singularities?", where an additional $x^2$ (or $z^2$) term is in front of the exponential factors. How would you go about this one? I am not sure the same solution as to the other problem applies, as the simplifications with the extra $z^2$ term might not be possible in a similar way. So what is the solution to $$ \oint z^2 \cdot \exp\Big(\frac{A}{z-1}\Big) \cdot \exp\Big(\frac{B}{z-2}\Big) dz$$ ? Again the contour can be as large as required. Any help or insight greatly appreciated.
2026-03-29 03:36:51.1774755411
Evaluate $\oint z^2 \cdot \exp\Big(\frac{A}{z-1}\Big) \cdot \exp\Big(\frac{B}{z-2}\Big) dz$
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