List questions from laurent-series

Published on 21 Mar 2016 - 18:37

189

Views

Laurent series expansion of $f(z)$ which converges for $\frac12 <|z|<1$

Published on 23 Mar 2016 - 16:19

49

Views

Understanding series convergence

Published on 23 Mar 2016 - 16:24

67

Views

Complex - Testing Convergence for $\sum_{n=1}^{\infty} n^{2}z^{n}$

Published on 26 Mar 2016 - 19:37

94

Views

Find the Laurent series of $\frac{1}{1+x^2}$ centered around $i$

Published on 28 Mar 2016 - 23:47

723

Views

Laurent series for $\cot(\pi z)/z^2$

Published on 28 Mar 2026 - 21:26

1.3k

Views

How to prove that field of rational functions is a proper subset of field of formal Laurent series?

Published on 30 Mar 2016 - 16:17

425

Views

Use a rectangular contour to evaluate the integral

Published on 30 Mar 2016 - 23:49

162

Views

Expressing $e^{-x}$ through a different series

Published on 31 Mar 2016 - 8:55

510

Views

Classify the singularities (removable, pole and essential)

Published on 02 Apr 2016 - 18:52

682

Views

Even and odd functions in Laurent decomposition

Published on 02 Apr 2016 - 20:55

649

Views

Classify the singularity - $\frac{1}{e^z-1}$

Published on 28 Mar 2026 - 4:24

88

Views

Classification of the singularities of $\frac{1}{z^2+1}$ at $a=1$

Published on 28 Mar 2026 - 4:28

465

Views

Expanding Laurent series

Published on 03 Apr 2016 - 1:47

213

Views

Classification of singularities - Pole

Published on 28 Mar 2026 - 4:31

List Question

Finding the Laurent series for $f(z)=\frac{z}{z-i}+\frac{z}{z+4}$.

Laurent series expansion of $f(z)$ which converges for $\frac12 <|z|<1$

Understanding series convergence

Complex - Testing Convergence for $\sum_{n=1}^{\infty} n^{2}z^{n}$

Find the Laurent series of $\frac{1}{1+x^2}$ centered around $i$

Laurent series for $\cot(\pi z)/z^2$

How to prove that field of rational functions is a proper subset of field of formal Laurent series?

Use a rectangular contour to evaluate the integral

Expressing $e^{-x}$ through a different series

Classify the singularities (removable, pole and essential)

Even and odd functions in Laurent decomposition

Classify the singularity - $\frac{1}{e^z-1}$

Classification of the singularities of $\frac{1}{z^2+1}$ at $a=1$

Expanding Laurent series

Classification of singularities - Pole

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