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 80 · Answer 2 · 2026-03-25 16:03:33

80

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

Published on 25 Mar 2026 - 16:03

score 329 · Answer 3 · 2026-05-10 17:34:07

329

Views

Closed form expression for an integral

Published on 10 May 2026 - 17:34

score 59 · Answer 4 · 2026-04-11 10:55:14

59

Views

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

Published on 11 Apr 2026 - 10:55

score 99 · Answer 5 · 2026-04-11 04:45:07

99

Views

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

Published on 11 Apr 2026 - 4:45

score 64 · Answer 6 · 2026-04-12 01:13:20

64

Views

Harmonic and Digamma function

Published on 12 Apr 2026 - 1:13

score 133 · Answer 7 · 2026-04-16 09:15:33

133

Views

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 16 Apr 2026 - 9:15

score 117 · Answer 8 · 2026-04-17 02:57:42

117

Views

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 17 Apr 2026 - 2:57

score 41 · Answer 9 · 2026-03-25 19:10:17

41

Views

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

Published on 25 Mar 2026 - 19:10

score 110 · Answer 10 · 2026-04-15 09:49:02

110

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 15 Apr 2026 - 9:49

score 33 · Answer 11 · 2026-04-12 01:42:50

33

Views

What are some formulas involving Dottie number and digamma function?

Published on 12 Apr 2026 - 1:42

score 159 · Answer 12 · 2026-04-15 07:13:47

159

Views

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

Published on 15 Apr 2026 - 7:13

score 77 · Answer 13 · 2026-04-15 19:22:04

77

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

Published on 15 Apr 2026 - 19:22

score 134 · Answer 14 · 2026-04-12 00:27:49

134

Views

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

Published on 12 Apr 2026 - 0:27

score 67 · Answer 15 · 2026-04-17 09:46:44

67

Views

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

Published on 17 Apr 2026 - 9:46

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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