Question

Sum $\sum _{k=0}^{\infty } \frac{(-1)^k \psi (k+1)}{\left(k-\frac{3}{2}\right)^2}$

score 144 · Answer 1 · 2026-03-25 04:00:10

144

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Sum $\sum _{k=0}^{\infty } \frac{(-1)^k \psi (k+1)}{\left(k-\frac{3}{2}\right)^2}$

Published on 25 Mar 2026 - 4:00

score 797 · Answer 2 · 2015-03-10 09:14:16

797

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Residue of $\Gamma^{2}$ and $\Gamma^{3}$

Published on 10 Mar 2015 - 9:14

score 1.3k · Answer 3 · 2015-03-18 10:28:45

1.3k

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Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$

Published on 18 Mar 2015 - 10:28

score 966 · Answer 4 · 2015-03-22 00:05:14

966

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Asymptotic behavior of the zeros of the digamma function

Published on 22 Mar 2015 - 0:05

score 59 · Answer 5 · 2015-04-09 12:11:18

59

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Solve for X in the given Equation(Gamma Curve)

Published on 09 Apr 2015 - 12:11

score 140 · Answer 6 · 2015-05-26 08:39:37

140

Views

Bounding infinite series derived from polygamma functions

Published on 26 May 2015 - 8:39

score 112 · Answer 7 · 2015-07-01 22:47:38

112

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Logarithmic Integral I

Published on 01 Jul 2015 - 22:47

score 489 · Answer 8 · 2015-07-11 04:02:39

489

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Re-Expressing the Digamma

Published on 11 Jul 2015 - 4:02

score 315 · Answer 9 · 2015-07-17 20:44:19

315

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Asymptotic behavior of the generalized polygamma function

Published on 17 Jul 2015 - 20:44

score 865 · Answer 10 · 2015-09-08 21:29:39

865

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Conjecture $\int_0^1\frac{\ln^2\left(1+x+x^2\right)}x dx\stackrel?=\frac{2\pi}{9\sqrt3}\psi^{(1)}(\tfrac13)-\frac{4\pi^3}{27\sqrt3}-\frac23\zeta(3)$

Published on 08 Sep 2015 - 21:29

score 1.2k · Answer 11 · 2015-09-09 23:17:55

1.2k

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Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

Published on 09 Sep 2015 - 23:17

score 972 · Answer 12 · 2026-03-25 10:56:03

972

Views

Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

Published on 25 Mar 2026 - 10:56

score 290 · Answer 13 · 2026-03-02 17:57:00

290

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Closed form for $\sum_{n=1}^{\infty} \frac{1}{1+n+n^2+\cdots+n^a}$

Published on 02 Mar 2026 - 17:57

score 156 · Answer 14 · 2026-02-28 03:01:25

156

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Minimizing $f(x)=A^{\frac{tx-1}{x-1}} \left( c^x \frac{\Gamma(0.5+x)}{\sqrt{\pi}} \right)^{\frac{1-t}{x-1}}$ subject to the constraint

Published on 28 Feb 2026 - 3:01

score 1k · Answer 15 · 2015-12-21 20:21:14

1k

Views

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

Published on 21 Dec 2015 - 20:21

List Question

Sum $\sum _{k=0}^{\infty } \frac{(-1)^k \psi (k+1)}{\left(k-\frac{3}{2}\right)^2}$

Residue of $\Gamma^{2}$ and $\Gamma^{3}$

Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$

Asymptotic behavior of the zeros of the digamma function

Solve for X in the given Equation(Gamma Curve)

Bounding infinite series derived from polygamma functions

Logarithmic Integral I

Re-Expressing the Digamma

Asymptotic behavior of the generalized polygamma function

Conjecture $\int_0^1\frac{\ln^2\left(1+x+x^2\right)}x dx\stackrel?=\frac{2\pi}{9\sqrt3}\psi^{(1)}(\tfrac13)-\frac{4\pi^3}{27\sqrt3}-\frac23\zeta(3)$

Integral ${\large\int}_0^1\ln^3\!\left(1+x+x^2\right)dx$

Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

Closed form for $\sum_{n=1}^{\infty} \frac{1}{1+n+n^2+\cdots+n^a}$

Minimizing $f(x)=A^{\frac{tx-1}{x-1}} \left( c^x \frac{\Gamma(0.5+x)}{\sqrt{\pi}} \right)^{\frac{1-t}{x-1}}$ subject to the constraint

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

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