Question

Expressions of G-BARNES

score 360 · Answer 1 · 2019-06-30 13:22:35

360

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Expressions of G-BARNES

Published on 30 Jun 2019 - 13:22

score 96 · Answer 2 · 2019-07-09 22:57:16

96

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Solving an integral with limits of polygamma functions

Published on 09 Jul 2019 - 22:57

score 428 · Answer 3 · 2019-08-23 06:59:27

428

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Compute $\sum_{n=1}^\infty (-1)^{n-1}\frac{H_{2n+1}}{(2n+1)^3}$ and $\sum_{n=1}^\infty (-1)^{n-1}\frac{H_{2n+1}^{(2)}}{(2n+1)^2}$

Published on 23 Aug 2019 - 6:59

score 89 · Answer 4 · 2019-09-02 05:45:50

89

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An simplified idenity from Mathematica involving polygamma

Published on 02 Sep 2019 - 5:45

score 142 · Answer 5 · 2019-09-13 20:03:39

142

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Prove $\lim_{n\ \mapsto\ \infty}4^n \psi^{(2)}(2^n)-\psi^{(2)}(1)=2\zeta(3)-1$

Published on 13 Sep 2019 - 20:03

score 838 · Answer 6 · 2019-09-15 07:51:35

838

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Integrating $\int_0^1\frac{\ln^2x\ln(1+x)}{1+x^2} dx$ using real methods

Published on 15 Sep 2019 - 7:51

score 520 · Answer 7 · 2019-09-21 20:51:15

520

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The closed-form of $\sum_{n=0}^{\infty}\frac{(-1)^n H^{(2)}_{n}}{(2n+1)^2} $

Published on 21 Sep 2019 - 20:51

score 102 · Answer 8 · 2014-07-05 19:30:09

102

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Is there a nice solution to the equation $\Psi(x)=\ln(\pi)$ with a positive real $x$?

Published on 05 Jul 2014 - 19:30

score 379 · Answer 9 · 2014-07-22 15:30:04

379

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How is $ \sum_{n=1}^{\infty}\left(\psi(\alpha n)-\log(\alpha n)+\frac{1}{2\alpha n}\right)$ when $\alpha$ is great?

Published on 22 Jul 2014 - 15:30

score 939 · Answer 10 · 2014-08-03 17:51:27

939

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A closed form of $\sum_{k=1}^\infty \psi^{(1)} (k+a)\psi^{(1)} (k+b)$?

Published on 03 Aug 2014 - 17:51

score 1.4k · Answer 11 · 2014-08-09 16:08:28

1.4k

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Derivative of Binomial Coefficient $\binom{2N}{N-x}$ with respect to $x$

Published on 09 Aug 2014 - 16:08

score 485 · Answer 12 · 2014-08-10 22:48:43

485

Views

Looking for an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$

Published on 10 Aug 2014 - 22:48

score 704 · Answer 13 · 2014-08-15 05:03:10

704

Views

Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$

Published on 15 Aug 2014 - 5:03

score 214 · Answer 14 · 2014-09-07 10:11:07

214

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Value of $\psi\left(\frac{1}{2}\right)$

Published on 07 Sep 2014 - 10:11

score 1k · Answer 15 · 2014-09-07 10:26:23

1k

Views

Evaluating $\int_0^{\Large\frac{\pi}{2}}\left(\frac{1}{\log(\tan x)}+\frac{1}{1-\tan(x)}\right)^3dx$

Published on 07 Sep 2014 - 10:26

List Question

Expressions of G-BARNES

Solving an integral with limits of polygamma functions

Compute $\sum_{n=1}^\infty (-1)^{n-1}\frac{H_{2n+1}}{(2n+1)^3}$ and $\sum_{n=1}^\infty (-1)^{n-1}\frac{H_{2n+1}^{(2)}}{(2n+1)^2}$

An simplified idenity from Mathematica involving polygamma

Prove $\lim_{n\ \mapsto\ \infty}4^n \psi^{(2)}(2^n)-\psi^{(2)}(1)=2\zeta(3)-1$

Integrating $\int_0^1\frac{\ln^2x\ln(1+x)}{1+x^2} dx$ using real methods

The closed-form of $\sum_{n=0}^{\infty}\frac{(-1)^n H^{(2)}_{n}}{(2n+1)^2} $

Is there a nice solution to the equation $\Psi(x)=\ln(\pi)$ with a positive real $x$?

How is $ \sum_{n=1}^{\infty}\left(\psi(\alpha n)-\log(\alpha n)+\frac{1}{2\alpha n}\right)$ when $\alpha$ is great?

A closed form of $\sum_{k=1}^\infty \psi^{(1)} (k+a)\psi^{(1)} (k+b)$?

Derivative of Binomial Coefficient $\binom{2N}{N-x}$ with respect to $x$

Looking for an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$

Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$

Value of $\psi\left(\frac{1}{2}\right)$

Evaluating $\int_0^{\Large\frac{\pi}{2}}\left(\frac{1}{\log(\tan x)}+\frac{1}{1-\tan(x)}\right)^3dx$

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