Question

Problem in calculating residue in analytic number theory of a function derived from Partition Function generated by Euler Infinite Product

score 85 · Answer 1 · 2019-12-12 17:23:46

85

Views

Problem in calculating residue in analytic number theory of a function derived from Partition Function generated by Euler Infinite Product

Published on 12 Dec 2019 - 17:23

score 725 · Answer 2 · 2026-03-26 17:32:32

725

Views

Proving that $\int_{0}^{\infty} \frac{\log(x) }{(1+x^2)^2}dx =- \frac{\pi}{4}$ using residues.

Published on 26 Mar 2026 - 17:32

score 208 · Answer 3 · 2026-03-28 05:59:26

208

Views

Looking for a proof for the value of the residue.

Published on 28 Mar 2026 - 5:59

score 38 · Answer 4 · 2026-03-28 12:03:00

38

Views

Calculation of residue at infinity and problem from Complex Variables, Mark J. Ablowitz

Published on 28 Mar 2026 - 12:03

score 143 · Answer 5 · 2019-12-18 16:43:20

143

Views

Theorem on residue of composite function

Published on 18 Dec 2019 - 16:43

score 467 · Answer 6 · 2019-12-22 14:13:18

467

Views

Find the residue of $f(z)=\frac{e^{az}}{1+e^z}$. at $\pi i$

Published on 22 Dec 2019 - 14:13

score 118 · Answer 7 · 2026-03-28 05:59:59

118

Views

Finding residues in a complex integral $\int_0^\infty\frac{z^6\,\mathrm{d}z}{(z^4+1)^2}$ using Laurent series expansion

Published on 28 Mar 2026 - 5:59

score 154 · Answer 8 · 2019-12-25 23:10:04

154

Views

How to calculate the integral $\int_0^{+\infty} \frac{\ln{x}}{(x+1)(x^2+1)} dx$ using residues?

Published on 25 Dec 2019 - 23:10

score 465 · Answer 9 · 2026-03-28 07:41:39

465

Views

Find all residues of all isolated singular points of the function $f(z) = \frac{1+z^{2n}}{z^n(z-a)}$, where $a \neq 0$ and $n \in \mathbb{Z}^+$

Published on 28 Mar 2026 - 7:41

score 48 · Answer 10 · 2019-12-31 16:27:23

48

Views

$\lim_{R\mapsto\infty}\int_{-R}^{+R}\frac{1}{x+i}\text{d}x=?$

Published on 31 Dec 2019 - 16:27

score 97 · Answer 11 · 2020-01-02 22:46:16

97

Views

Contour Integral of a rational function with complex denominator: $\int_{-\infty}^{\infty} \frac{e^{ibx}}{x^2+a^2} dx$

Published on 02 Jan 2020 - 22:46

score 5.2k · Answer 12 · 2020-01-03 15:32:54

5.2k

Views

Compute the residue of $ 1/(\sin z) $ at $z=\pi$

Published on 03 Jan 2020 - 15:32

score 68 · Answer 13 · 2020-01-04 17:23:45

68

Views

Solution verification: $2851^{604^{20}}\overset{\text{?}} \equiv\pmod{14}$

Published on 04 Jan 2020 - 17:23

score 150 · Answer 14 · 2026-03-26 17:31:42

150

Views

Sum of roots with residue theorem

Published on 26 Mar 2026 - 17:31

score 2.8k · Answer 15 · 2020-01-06 22:19:00

2.8k

Views

Residue Theorem if Pole is on Contour

Published on 06 Jan 2020 - 22:19

List Question

Problem in calculating residue in analytic number theory of a function derived from Partition Function generated by Euler Infinite Product

Proving that $\int_{0}^{\infty} \frac{\log(x) }{(1+x^2)^2}dx =- \frac{\pi}{4}$ using residues.

Looking for a proof for the value of the residue.

Calculation of residue at infinity and problem from Complex Variables, Mark J. Ablowitz

Theorem on residue of composite function

Find the residue of $f(z)=\frac{e^{az}}{1+e^z}$. at $\pi i$

Finding residues in a complex integral $\int_0^\infty\frac{z^6\,\mathrm{d}z}{(z^4+1)^2}$ using Laurent series expansion

How to calculate the integral $\int_0^{+\infty} \frac{\ln{x}}{(x+1)(x^2+1)} dx$ using residues?

Find all residues of all isolated singular points of the function $f(z) = \frac{1+z^{2n}}{z^n(z-a)}$, where $a \neq 0$ and $n \in \mathbb{Z}^+$

$\lim_{R\mapsto\infty}\int_{-R}^{+R}\frac{1}{x+i}\text{d}x=?$

Contour Integral of a rational function with complex denominator: $\int_{-\infty}^{\infty} \frac{e^{ibx}}{x^2+a^2} dx$

Compute the residue of $ 1/(\sin z) $ at $z=\pi$

Solution verification: $2851^{604^{20}}\overset{\text{?}} \equiv\pmod{14}$

Sum of roots with residue theorem

Residue Theorem if Pole is on Contour

Trending Questions

Popular # Hahtags

Popular Questions