All Questions
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Contour integral over function $P(x)/Q(x)$: $P(x) = 1$ and $Q(x)$ can be broken into linear factors
a. Let $z_1,z_2,...,z_n$ be distinct complex numbers $(n \geq 2)$. Show that in the partial fractions decomposition
\begin{equation}
\frac{1}{(z-z_1)(z-z_2)\cdots(z-z_n)} = \frac{A_1}{z-z_1}+\frac{A_2}...
- 142
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Mistake in the computation via partial fractions
This is a computation made in Titchmash's Introduction to Zeta functions. I was trying to reverse the computation. However, I kept missing factors.
Consider $\frac{1- xyz^2}{(1-z)(1-xz)(1-yz)(1-xyz)}...
- 8,550
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Partial Fractions and Complex Integral
I have $\int_{C}\frac{e^z}{z^2 + a^2}$ where $a>0$ and $C$ is a positively oriented simple closed contour containing the circle $|z|=1$.
I start with
$$\frac{1}{z^2 + a^2} = \frac{1}{(z+ia)(z-ia)...
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