Question

Find the function $f(x)=\sum_{n=1}^{\infty}\frac{H_{n-1}(-x)^n}{n!}$

score 88 · Answer 1 · 2026-03-25 09:32:05

88

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Find the function $f(x)=\sum_{n=1}^{\infty}\frac{H_{n-1}(-x)^n}{n!}$

Published on 25 Mar 2026 - 9:32

score 127 · Answer 2 · 2020-05-07 17:02:28

127

Views

Integral $\int_0^1 \frac{\ln(\sin(x))}{\sqrt{x}}$

Published on 07 May 2020 - 17:02

score 102 · Answer 3 · 2026-03-30 08:03:02

102

Views

Calculating the improper integral $\int_{0}^{+\infty}\frac{\log \mid 1-x^2 \mid}{x^2} dx$

Published on 30 Mar 2026 - 8:03

score 85 · Answer 4 · 2026-04-06 02:54:15

85

Views

Prove $f(x)=\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is Improper Riemann Integrable

Published on 06 Apr 2026 - 2:54

score 86 · Answer 5 · 2020-05-08 13:33:14

86

Views

Convergence test for integral (between -infinty to +infinty)

Published on 08 May 2020 - 13:33

score 350 · Answer 6 · 2020-05-09 18:49:18

350

Views

How to prove $\int^{\infty}_{0} e^{-\alpha x} f(x)dx \rightarrow \int ^{\infty}_{0} f(x) dx$ when $\alpha \rightarrow 0$?

Published on 09 May 2020 - 18:49

score 162 · Answer 7 · 2020-05-10 21:11:30

162

Views

Showing divergence of the integral of a periodic function

Published on 10 May 2020 - 21:11

score 80 · Answer 8 · 2020-05-10 21:55:11

80

Views

find for which $\alpha, \beta$ does $\int\limits_{100}^{\infty}\frac{1}{xln(x)^{\alpha}ln(ln(x))^{\beta}}dx$ converge

Published on 10 May 2020 - 21:55

score 59 · Answer 9 · 2020-05-11 11:15:54

$f$ Continuously differentiable twice on $[0, 1]$, $\int\limits_0^1 \frac{(f(x)-1)^2-4x^2}{x^\frac{7}{2}}dx$ converges, calculate $f(0), |f'(0)|$

score 36 · Answer 10 · 2020-05-12 12:38:51

36

Views

Understanding a proof of absolute convergence of an Integral

Published on 12 May 2020 - 12:38

score 125 · Answer 11 · 2020-05-12 13:35:45

125

Views

Showing for which parameter values an improper integral of $\ln(1+x^2)/x^\alpha$ converges

Published on 12 May 2020 - 13:35

score 55 · Answer 12 · 2020-05-13 10:01:34

55

Views

Integral $ \int_E \frac{1}{x^ay^b}dxdy \qquad E={x>0,y>0,xy \geq 1}$

Published on 13 May 2020 - 10:01

score 139 · Answer 13 · 2020-05-13 10:20:19

139

Views

Integral $\int _1^{\infty }\sin^2 \left(\frac{3}{x} \right)dx$

Published on 13 May 2020 - 10:20

score 71 · Answer 14 · 2020-05-13 12:41:52

71

Views

Does $\int_{2018}^{\infty} \frac{\cos x}{x + x^{1/3}\sin^2x}\mathrm dx$ converge / diverge

Published on 13 May 2020 - 12:41

score 48 · Answer 15 · 2020-05-13 20:02:02

48

Views

$\int_{\mathbb{R}^2} e^{-(2|x|^a+3|y|^b)}dxdy$

Published on 13 May 2020 - 20:02

List Question

Find the function $f(x)=\sum_{n=1}^{\infty}\frac{H_{n-1}(-x)^n}{n!}$

Integral $\int_0^1 \frac{\ln(\sin(x))}{\sqrt{x}}$

Calculating the improper integral $\int_{0}^{+\infty}\frac{\log \mid 1-x^2 \mid}{x^2} dx$

Prove $f(x)=\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is Improper Riemann Integrable

Convergence test for integral (between -infinty to +infinty)

How to prove $\int^{\infty}_{0} e^{-\alpha x} f(x)dx \rightarrow \int ^{\infty}_{0} f(x) dx$ when $\alpha \rightarrow 0$?

Showing divergence of the integral of a periodic function

find for which $\alpha, \beta$ does $\int\limits_{100}^{\infty}\frac{1}{xln(x)^{\alpha}ln(ln(x))^{\beta}}dx$ converge

$f$ Continuously differentiable twice on $[0, 1]$, $\int\limits_0^1 \frac{(f(x)-1)^2-4x^2}{x^\frac{7}{2}}dx$ converges, calculate $f(0), |f'(0)|$

Understanding a proof of absolute convergence of an Integral

Showing for which parameter values an improper integral of $\ln(1+x^2)/x^\alpha$ converges

Integral $ \int_E \frac{1}{x^ay^b}dxdy \qquad E={x>0,y>0,xy \geq 1}$

Integral $\int _1^{\infty }\sin^2 \left(\frac{3}{x} \right)dx$

Does $\int_{2018}^{\infty} \frac{\cos x}{x + x^{1/3}\sin^2x}\mathrm dx$ converge / diverge

$\int_{\mathbb{R}^2} e^{-(2|x|^a+3|y|^b)}dxdy$

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