Question

Approximating the Digamma function for small arguments

score 304 · Answer 1 · 2026-04-12 11:49:40

304

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Approximating the Digamma function for small arguments

Published on 12 Apr 2026 - 11:49

score 250 · Answer 2 · 2026-04-12 14:42:02

250

Views

Showing the existence of the Euler-Mascheroni constant

Published on 12 Apr 2026 - 14:42

score 174 · Answer 3 · 2026-04-17 00:48:34

174

Views

Sum a product of Bernoulli numbers and binomial coefficients

Published on 17 Apr 2026 - 0:48

score 435 · Answer 4 · 2026-04-12 17:29:07

435

Views

Sum with Digamma function expressed by hypergeometric function?

Published on 12 Apr 2026 - 17:29

score 307 · Answer 5 · 2026-04-13 23:05:08

307

Views

Evaluating an infinite series containing Digamma Function

Published on 13 Apr 2026 - 23:05

score 83 · Answer 6 · 2026-04-07 21:33:53

83

Views

Show an inequality about digamma function

Published on 07 Apr 2026 - 21:33

score 89 · Answer 7 · 2026-04-14 07:10:34

89

Views

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

Published on 14 Apr 2026 - 7:10

score 239 · Answer 8 · 2026-04-16 00:47:27

239

Views

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

Published on 16 Apr 2026 - 0:47

score 121 · Answer 9 · 2026-05-10 23:38:27

121

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 10 May 2026 - 23:38

score 382 · Answer 10 · 2026-04-16 13:44:55

382

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 16 Apr 2026 - 13:44

score 290 · Answer 11 · 2026-04-15 11:40:27

290

Views

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

Published on 15 Apr 2026 - 11:40

score 78 · Answer 12 · 2026-04-14 06:37:58

78

Views

Use of digamma function to evaluate some finite series

Published on 14 Apr 2026 - 6:37

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 112 · Answer 14 · 2026-04-14 22:54:10

112

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 14 Apr 2026 - 22:54

score 75 · Answer 15 · 2026-04-17 03:52:33

75

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 17 Apr 2026 - 3:52

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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