List questions from residue-calculus

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Compute the given integral with residue theorem

Published on 05 Jun 2018 - 14:21

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Taking residues from complex logarithms

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Compute derivative of $\frac{f(z)}{f'(z)}$ at a root of $f(z)$.

Published on 06 Jun 2018 - 21:45

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Lagrange Inversion Theorem Proof

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A function with $R_0(f)=\sum_{n\ge0} \frac{1}{n!(n+1)!}$

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Show that $\int_{0}^{2\pi}\frac{1}{1+\alpha\cos^2(t)}dt=\frac{2\pi}{\sqrt{\lambda+1}}$ with $\alpha>-1$.

Published on 14 Jun 2018 - 16:51

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Evaluating the complex integral $\int_{0}^{\infty} \frac {\sin (\ln x) dx }{x^2 + 4} $

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Complex Integral with Similar Integrands Yielding Very Different Results

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The Maclaurin Series for holomorphic function f

Published on 17 Jun 2018 - 20:24

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Problem with computing residues

Published on 19 Jun 2018 - 1:04

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limit at infinity of a meromorphic function using residues

Published on 20 Jun 2018 - 7:23

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Contour Integration of a simple expression

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Residue identity for function composition: $ \operatorname{Res}(f; h(a)) = \operatorname{Res}((f∘h)h'; a)$

Published on 24 Jun 2018 - 8:25

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Improper integrals with residue theorem

Published on 26 Jun 2018 - 11:34

List Question

What is the Laurent series expansion of $e^{-e^{\frac {1} {z}}}$ about $z=0$?

Compute the given integral with residue theorem

Taking residues from complex logarithms

Compute derivative of $\frac{f(z)}{f'(z)}$ at a root of $f(z)$.

Lagrange Inversion Theorem Proof

A function with $R_0(f)=\sum_{n\ge0} \frac{1}{n!(n+1)!}$

Show that $\int_{0}^{2\pi}\frac{1}{1+\alpha\cos^2(t)}dt=\frac{2\pi}{\sqrt{\lambda+1}}$ with $\alpha>-1$.

Evaluating the complex integral $\int_{0}^{\infty} \frac {\sin (\ln x) dx }{x^2 + 4} $

Complex Integral with Similar Integrands Yielding Very Different Results

The Maclaurin Series for holomorphic function f

Problem with computing residues

limit at infinity of a meromorphic function using residues

Contour Integration of a simple expression

Residue identity for function composition: $ \operatorname{Res}(f; h(a)) = \operatorname{Res}((f∘h)h'; a)$

Improper integrals with residue theorem

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