Question

Approximating the Digamma function for small arguments

score 301 · Answer 1 · 2021-06-28 13:02:57

301

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Approximating the Digamma function for small arguments

Published on 28 Jun 2021 - 13:02

score 247 · Answer 2 · 2021-07-01 00:21:28

247

Views

Showing the existence of the Euler-Mascheroni constant

Published on 01 Jul 2021 - 0:21

score 169 · Answer 3 · 2021-07-05 18:16:43

169

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Sum a product of Bernoulli numbers and binomial coefficients

Published on 05 Jul 2021 - 18:16

score 432 · Answer 4 · 2021-07-10 18:38:14

432

Views

Sum with Digamma function expressed by hypergeometric function?

Published on 10 Jul 2021 - 18:38

score 304 · Answer 5 · 2021-07-11 06:56:29

304

Views

Evaluating an infinite series containing Digamma Function

Published on 11 Jul 2021 - 6:56

score 81 · Answer 6 · 2021-07-30 03:54:39

81

Views

Show an inequality about digamma function

Published on 30 Jul 2021 - 3:54

score 86 · Answer 7 · 2021-08-19 12:28:18

86

Views

What's the easiest way to derive an approximation of $ \frac{d}{dz} \log \Gamma(z) $ from the literature?

Published on 19 Aug 2021 - 12:28

score 236 · Answer 8 · 2021-08-22 19:45:13

236

Views

Computing $\sum_{n=2}^{\infty}\frac{1}{(n^2-1)^2}=\frac{\pi^2}{12}-\frac{11}{16}$

Published on 22 Aug 2021 - 19:45

score 120 · Answer 9 · 2026-03-25 20:36:05

120

Views

Ask for a proof of logarithmically complete monotonicity of a power-exponential function involving the difference of the psi and logarithmic functions

Published on 25 Mar 2026 - 20:36

score 379 · Answer 10 · 2021-10-05 19:30:19

379

Views

Mistake computing $\int_0^\infty\frac{x \ln(1+x^2)}{\sinh \pi x}\,dx=\frac{\ln 2}{3} - \log \pi - \frac{1}{2} + 6 \ln A $

Published on 05 Oct 2021 - 19:30

score 288 · Answer 11 · 2021-11-03 17:15:09

288

Views

$\frac {\zeta(2)}{e^2} + \frac {\zeta(3)}{e^3} + \frac {\zeta(4)}{e^4} + \frac {\zeta(5)}{e^5}.....?$

Published on 03 Nov 2021 - 17:15

score 75 · Answer 12 · 2021-11-21 14:29:20

75

Views

Use of digamma function to evaluate some finite series

Published on 21 Nov 2021 - 14:29

score 71 · Answer 13 · 2026-03-25 20:34:45

71

Views

Simplification of a difficult identity involving the digamma function

Published on 25 Mar 2026 - 20:34

score 109 · Answer 14 · 2021-11-30 12:32:18

109

Views

Is there a more elementary way to arrive at: $\ln(m)=\lim_{n\to\infty}\sum_{k=n+1}^{mn}\frac{1}{k}$?

Published on 30 Nov 2021 - 12:32

score 72 · Answer 15 · 2021-12-21 15:59:01

72

Views

Find a function $\phi(a)$ which fixes the area under $f(x)=x^a e^{-\phi(a)x}$ for all $a>0$

Published on 21 Dec 2021 - 15:59

List Question

Approximating the Digamma function for small arguments

Showing the existence of the Euler-Mascheroni constant

Sum a product of Bernoulli numbers and binomial coefficients

Sum with Digamma function expressed by hypergeometric function?

Evaluating an infinite series containing Digamma Function

Show an inequality about digamma function

What's the easiest way to derive an approximation of $ \frac{d}{dz} \log \Gamma(z) $ from the literature?

Computing $\sum_{n=2}^{\infty}\frac{1}{(n^2-1)^2}=\frac{\pi^2}{12}-\frac{11}{16}$

Ask for a proof of logarithmically complete monotonicity of a power-exponential function involving the difference of the psi and logarithmic functions

Mistake computing $\int_0^\infty\frac{x \ln(1+x^2)}{\sinh \pi x}\,dx=\frac{\ln 2}{3} - \log \pi - \frac{1}{2} + 6 \ln A $

$\frac {\zeta(2)}{e^2} + \frac {\zeta(3)}{e^3} + \frac {\zeta(4)}{e^4} + \frac {\zeta(5)}{e^5}.....?$

Use of digamma function to evaluate some finite series

Simplification of a difficult identity involving the digamma function

Is there a more elementary way to arrive at: $\ln(m)=\lim_{n\to\infty}\sum_{k=n+1}^{mn}\frac{1}{k}$?

Find a function $\phi(a)$ which fixes the area under $f(x)=x^a e^{-\phi(a)x}$ for all $a>0$

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