Question

Variants of geometric sum formula

score 29 · Answer 1 · 2026-03-26 12:34:59

29

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Variants of geometric sum formula

Published on 26 Mar 2026 - 12:34

score 134 · Answer 2 · 2026-03-28 23:58:44

134

Views

How to evaluate $\sum_{n=1}^{\infty}\frac{H_{n}^{(2)}}{n^{4}}$

Published on 28 Mar 2026 - 23:58

score 138 · Answer 3 · 2024-02-24 06:15:01

138

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How to evaluate $\int_{0}^{1} \int_{0}^{1} \frac{{(1 + x) \cdot \log(x) - (1 + y) \cdot \log(y)}}{{x - y}} \cdot (1 + \log(xy)) \,dy \,dx$

Published on 24 Feb 2024 - 6:15

score 316 · Answer 4 · 2024-02-25 19:03:02

316

Views

Why is none trying to find the value of $\displaystyle\sum_{n=1}^\infty\frac1{n^n}$?

Published on 25 Feb 2024 - 19:03

score 135 · Answer 5 · 2026-03-26 12:47:54

135

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Improper Integral $\int_{0}^{\infty} \log(t) t^{-\frac{1}{2}} \exp\left\{-t\right\} dt$

Published on 26 Mar 2026 - 12:47

score 220 · Answer 6 · 2024-02-28 21:08:25

220

Views

Remarkable logarithmic integral $\int_0^1 \frac{x \log ^2(x) \log (1-x)}{1+x^2} dx$

Published on 28 Feb 2024 - 21:08

score 58 · Answer 7 · 2026-04-01 10:35:03

58

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Closed form of ${_2}{F}_1\left(\frac{1}{2},s,\frac{3}{2};-\frac{1}{a^2}\right)$

Published on 01 Apr 2026 - 10:35

score 95 · Answer 8 · 2024-03-09 12:58:18

95

Views

How to integrate $\int_{2}^{\infty} \frac{\pi(x) \ln(x^{\sqrt{x}}) \cdot (x^2 + 1)}{(x^2 - 1)^3} \,dx$

Published on 09 Mar 2024 - 12:58

score 552 · Answer 9 · 2024-03-10 10:15:26

552

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Show that $\int_{\arccos(1/4)}^{\pi/2}\arccos(\cos x (2\sin^2x+\sqrt{1+4\sin^4x})) \mathrm dx=\frac{\pi^2}{40}$

Published on 10 Mar 2024 - 10:15

score 102 · Answer 10 · 2024-03-11 04:05:24

102

Views

Please help me identify any errors in my solution to the following DE: $xf(x)-f'(x)=0$, $f(0)=1$

Published on 11 Mar 2024 - 4:05

score 38 · Answer 11 · 2026-04-01 12:46:23

38

Views

Multivariable non-linear ODE with sine and cosine.

Published on 01 Apr 2026 - 12:46

score 31 · Answer 12 · 2026-03-26 01:14:47

31

Views

Why does the poisson regression beta coefficient ML estimate have no closed form solution?

Published on 26 Mar 2026 - 1:14

score 216 · Answer 13 · 2026-03-26 12:37:31

216

Views

Closed form of $\int_{x}^{1}\left(1-s\right)^{-1/2}P_{m}^{\left(1/2,-1/2\right)}\left(s\right)ds$

Published on 26 Mar 2026 - 12:37

score 232 · Answer 14 · 2024-03-16 06:43:28

232

Views

Is it possible to evaluate $\int_{0}^{\frac{\pi}{2}} e^{-(\pi \tan(x) - 1)^2} \, dx$?

Published on 16 Mar 2024 - 6:43

score 54 · Answer 15 · 2026-03-26 17:34:52

54

Views

Indefinite integral of elliptic integrals

Published on 26 Mar 2026 - 17:34

List Question

Variants of geometric sum formula

How to evaluate $\sum_{n=1}^{\infty}\frac{H_{n}^{(2)}}{n^{4}}$

How to evaluate $\int_{0}^{1} \int_{0}^{1} \frac{{(1 + x) \cdot \log(x) - (1 + y) \cdot \log(y)}}{{x - y}} \cdot (1 + \log(xy)) \,dy \,dx$

Why is none trying to find the value of $\displaystyle\sum_{n=1}^\infty\frac1{n^n}$?

Improper Integral $\int_{0}^{\infty} \log(t) t^{-\frac{1}{2}} \exp\left\{-t\right\} dt$

Remarkable logarithmic integral $\int_0^1 \frac{x \log ^2(x) \log (1-x)}{1+x^2} dx$

Closed form of ${_2}{F}_1\left(\frac{1}{2},s,\frac{3}{2};-\frac{1}{a^2}\right)$

How to integrate $\int_{2}^{\infty} \frac{\pi(x) \ln(x^{\sqrt{x}}) \cdot (x^2 + 1)}{(x^2 - 1)^3} \,dx$

Show that $\int_{\arccos(1/4)}^{\pi/2}\arccos(\cos x (2\sin^2x+\sqrt{1+4\sin^4x})) \mathrm dx=\frac{\pi^2}{40}$

Please help me identify any errors in my solution to the following DE: $xf(x)-f'(x)=0$, $f(0)=1$

Multivariable non-linear ODE with sine and cosine.

Why does the poisson regression beta coefficient ML estimate have no closed form solution?

Closed form of $\int_{x}^{1}\left(1-s\right)^{-1/2}P_{m}^{\left(1/2,-1/2\right)}\left(s\right)ds$

Is it possible to evaluate $\int_{0}^{\frac{\pi}{2}} e^{-(\pi \tan(x) - 1)^2} \, dx$?

Indefinite integral of elliptic integrals

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