Question

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

score 144 · Answer 1 · 2026-03-25 11:09:43

144

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Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

Published on 25 Mar 2026 - 11:09

score 79 · Answer 2 · 2023-02-24 21:25:37

79

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What is the exact value of $\sum\limits_{n=1}^\infty \frac{1}{F_n}$?

Published on 24 Feb 2023 - 21:25

score 327 · Answer 3 · 2023-02-26 16:50:17

327

Views

Closed form expression for an integral

Published on 26 Feb 2023 - 16:50

score 56 · Answer 4 · 2023-03-06 15:44:17

56

Views

Finding the local extrema of $x^{\frac{x}{x!}}$

Published on 06 Mar 2023 - 15:44

score 96 · Answer 5 · 2023-04-09 16:47:17

96

Views

Having trouble evaluating an integral with logarithm and binomial expansion to difference of digamma functions

Published on 09 Apr 2023 - 16:47

score 61 · Answer 6 · 2023-04-10 00:55:12

61

Views

Harmonic and Digamma function

Published on 10 Apr 2023 - 0:55

score 130 · Answer 7 · 2023-06-10 16:16:47

130

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Proving $\sum_{k=1}^\infty\left(\frac{(n^k+1)}{(n+1)^k}\zeta(k+1)\right)=\psi(\frac{n}{n+1})-\psi(\frac{1}{n+1})=\pi\cot(\frac{\pi}{n+1})$

Published on 10 Jun 2023 - 16:16

score 114 · Answer 8 · 2023-06-24 09:40:55

114

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Showing $\displaystyle{\frac{\psi(z)}{\Gamma(z)}=-e^{2\gamma z}\prod_{k=0}^{\infty}\left(1-\frac{z}{x_k}\right)e^{z/x_k}}$

Published on 24 Jun 2023 - 9:40

score 40 · Answer 9 · 2023-06-27 05:36:24

40

Views

What is the intersection point of the graphs of digamma and trigamma functions?

Published on 27 Jun 2023 - 5:36

score 107 · Answer 10 · 2023-07-13 19:22:06

107

Views

Does $\sum_{r = 1}^n \ln\left(\frac{1 + r}{r}\right) = \ln (\Gamma(n + 2)) - \ln (\Gamma(n+1))$? If so, why?

Published on 13 Jul 2023 - 19:22

score 30 · Answer 11 · 2023-07-29 08:43:48

30

Views

What are some formulas involving Dottie number and digamma function?

Published on 29 Jul 2023 - 8:43

score 156 · Answer 12 · 2023-08-06 00:29:42

156

Views

How to finish the integral $\int_{0}^{\infty}\frac{\sin(x)}{\sinh(x)}\,dx$

Published on 06 Aug 2023 - 0:29

score 74 · Answer 13 · 2023-08-08 16:06:19

74

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Series expansion for $\displaystyle{\psi(t+2)-\psi\left(\frac{t+3}{2}\right)}$

Published on 08 Aug 2023 - 16:06

score 133 · Answer 14 · 2026-02-24 00:29:04

133

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About the integral $\int_0^{\pi/2} (\sin x-1)/\ln(\sin x) \mathrm{d}x$

Published on 24 Feb 2026 - 0:29

score 64 · Answer 15 · 2023-09-29 16:58:11

64

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Do we have $\log\Gamma(2x+1)-2\log\Gamma(x+1)\ge\log(x^2+1)$ for $x\in[0,1]$?

Published on 29 Sep 2023 - 16:58

List Question

Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$

What is the exact value of $\sum\limits_{n=1}^\infty \frac{1}{F_n}$?

Closed form expression for an integral

Finding the local extrema of $x^{\frac{x}{x!}}$

Having trouble evaluating an integral with logarithm and binomial expansion to difference of digamma functions

Harmonic and Digamma function

Proving $\sum_{k=1}^\infty\left(\frac{(n^k+1)}{(n+1)^k}\zeta(k+1)\right)=\psi(\frac{n}{n+1})-\psi(\frac{1}{n+1})=\pi\cot(\frac{\pi}{n+1})$

Showing $\displaystyle{\frac{\psi(z)}{\Gamma(z)}=-e^{2\gamma z}\prod_{k=0}^{\infty}\left(1-\frac{z}{x_k}\right)e^{z/x_k}}$

What is the intersection point of the graphs of digamma and trigamma functions?

Does $\sum_{r = 1}^n \ln\left(\frac{1 + r}{r}\right) = \ln (\Gamma(n + 2)) - \ln (\Gamma(n+1))$? If so, why?

What are some formulas involving Dottie number and digamma function?

How to finish the integral $\int_{0}^{\infty}\frac{\sin(x)}{\sinh(x)}\,dx$

Series expansion for $\displaystyle{\psi(t+2)-\psi\left(\frac{t+3}{2}\right)}$

About the integral $\int_0^{\pi/2} (\sin x-1)/\ln(\sin x) \mathrm{d}x$

Do we have $\log\Gamma(2x+1)-2\log\Gamma(x+1)\ge\log(x^2+1)$ for $x\in[0,1]$?

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