Question

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

score 53 · Answer 1 · 2026-04-10 21:51:58

53

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

Published on 10 Apr 2026 - 21:51

score 89 · Answer 2 · 2026-04-12 21:27:05

89

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

Published on 12 Apr 2026 - 21:27

score 130 · Answer 3 · 2026-04-14 16:40:36

130

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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 14 Apr 2026 - 16:40

score 114 · Answer 4 · 2026-04-16 15:01:19

114

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

Published on 16 Apr 2026 - 15:01

score 105 · Answer 5 · 2026-04-14 08:27:56

105

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

Published on 14 Apr 2026 - 8:27

score 67 · Answer 6 · 2026-04-13 20:30:10

67

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

Published on 13 Apr 2026 - 20:30

score 324 · Answer 7 · 2026-04-14 12:22:38

324

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

Published on 14 Apr 2026 - 12:22

score 192 · Answer 8 · 2026-05-10 22:10:22

192

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

Published on 10 May 2026 - 22:10

score 444 · Answer 9 · 2026-04-13 17:32:46

444

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

Published on 13 Apr 2026 - 17:32

score 110 · Answer 10 · 2026-04-16 13:32:17

110

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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 16 Apr 2026 - 13:32

score 93 · Answer 11 · 2026-04-12 07:45:43

93

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

Published on 12 Apr 2026 - 7:45

score 61 · Answer 12 · 2026-04-17 05:21:42

61

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Derivation step in paper on LDA

Published on 17 Apr 2026 - 5:21

score 137 · Answer 13 · 2026-04-13 05:47:53

137

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Digamma function Identities

Published on 13 Apr 2026 - 5:47

score 257 · Answer 14 · 2026-04-17 13:48:49

257

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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 17 Apr 2026 - 13:48

score 1k · Answer 15 · 2026-04-11 13:29:28

1k

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Asymptotic Expansion of Digamma Function

Published on 11 Apr 2026 - 13:29

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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