Question

Finite sum of reciprocals of odd integers in terms of digamma function

score 50 · Answer 1 · 2020-10-21 03:36:46

50

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Finite sum of reciprocals of odd integers in terms of digamma function

Published on 21 Oct 2020 - 3:36

score 86 · Answer 2 · 2020-10-24 08:03:26

86

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Is $\psi(x)-\log x$ strictly increasing for strictly positive $x$?

Published on 24 Oct 2020 - 8:03

score 127 · Answer 3 · 2020-10-28 20:53:33

127

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Does there exist a formula for $\int_0^{\infty} t^{k} {\tt sech}(t)dt$ that is correct whenever the real part of k is greater than negative 1?

Published on 28 Oct 2020 - 20:53

score 111 · Answer 4 · 2020-11-02 14:59:35

111

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Dimension over $\mathbb{Q}$ of infinite sums of rational functions

Published on 02 Nov 2020 - 14:59

score 102 · Answer 5 · 2020-11-03 07:30:22

102

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Deriving closed form of $\sum_{n=1}^\infty\frac{(-1)^{n+1}\ln(n+1)}{n} $

Published on 03 Nov 2020 - 7:30

score 64 · Answer 6 · 2020-11-26 11:43:14

64

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Why does $\frac{d}{d\nu}\ln\Gamma\left(\frac{\nu}{2}\right)$ simplify to digamma function?

Published on 26 Nov 2020 - 11:43

score 321 · Answer 7 · 2020-12-11 07:06:16

321

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Closed form of the sum $\sum_{r\ge2}\frac{\zeta(r)}{r^2}$

Published on 11 Dec 2020 - 7:06

score 190 · Answer 8 · 2020-12-12 04:31:12

190

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A convergent series for the Trigamma function $\psi_1(n) =\sum_{k=n}^{\infty} \frac1{k^2} $

Published on 12 Dec 2020 - 4:31

score 441 · Answer 9 · 2020-12-13 12:22:10

441

Views

Closed form of the sum $\sum_{n=1}^{\infty}\frac{H_n}{n^x}$

Published on 13 Dec 2020 - 12:22

score 107 · Answer 10 · 2020-12-20 02:15:07

107

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Why does $\operatorname{Im}\psi\left(\frac{1}{2}+i x\right)=\frac{\pi}{2}\tanh(\pi x)$, and what can be said of the real part?

Published on 20 Dec 2020 - 2:15

score 90 · Answer 11 · 2020-12-23 17:43:25

90

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Using calculus to find the maximum involving digamma function (in Latent Dirichlet Allocation).

Published on 23 Dec 2020 - 17:43

score 56 · Answer 12 · 2021-01-04 22:15:00

56

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Derivation step in paper on LDA

Published on 04 Jan 2021 - 22:15

score 134 · Answer 13 · 2021-01-08 04:56:32

134

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Digamma function Identities

Published on 08 Jan 2021 - 4:56

score 254 · Answer 14 · 2021-01-27 16:16:03

254

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Evaluating $I(z,s)=\int_0^1\int_0^1\left(1-\frac{(1-x)(1-y)}{(1-(1-z)x)(1-(1-z)y)}\right)^{s-2}\,\mathrm dx\mathrm dy$

Published on 27 Jan 2021 - 16:16

score 1k · Answer 15 · 2021-02-12 05:50:24

1k

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Asymptotic Expansion of Digamma Function

Published on 12 Feb 2021 - 5:50

List Question

Finite sum of reciprocals of odd integers in terms of digamma function

Is $\psi(x)-\log x$ strictly increasing for strictly positive $x$?

Does there exist a formula for $\int_0^{\infty} t^{k} {\tt sech}(t)dt$ that is correct whenever the real part of k is greater than negative 1?

Dimension over $\mathbb{Q}$ of infinite sums of rational functions

Deriving closed form of $\sum_{n=1}^\infty\frac{(-1)^{n+1}\ln(n+1)}{n} $

Why does $\frac{d}{d\nu}\ln\Gamma\left(\frac{\nu}{2}\right)$ simplify to digamma function?

Closed form of the sum $\sum_{r\ge2}\frac{\zeta(r)}{r^2}$

A convergent series for the Trigamma function $\psi_1(n) =\sum_{k=n}^{\infty} \frac1{k^2} $

Closed form of the sum $\sum_{n=1}^{\infty}\frac{H_n}{n^x}$

Why does $\operatorname{Im}\psi\left(\frac{1}{2}+i x\right)=\frac{\pi}{2}\tanh(\pi x)$, and what can be said of the real part?

Using calculus to find the maximum involving digamma function (in Latent Dirichlet Allocation).

Derivation step in paper on LDA

Digamma function Identities

Evaluating $I(z,s)=\int_0^1\int_0^1\left(1-\frac{(1-x)(1-y)}{(1-(1-z)x)(1-(1-z)y)}\right)^{s-2}\,\mathrm dx\mathrm dy$

Asymptotic Expansion of Digamma Function

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