Question

Alternative form to express the second derivative of $\zeta (2) $

score 550 · Answer 1 · 2016-08-29 20:47:36

550

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Alternative form to express the second derivative of $\zeta (2) $

Published on 29 Aug 2016 - 20:47

score 2.1k · Answer 2 · 2016-08-30 18:56:35

2.1k

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Finding a closed form for binomial coefficient summation

Published on 30 Aug 2016 - 18:56

score 162 · Answer 3 · 2016-08-30 21:55:09

162

Views

Is $\sum_{n=1}^\infty \ln \left(1-\frac{1}{p_n^s} \right)=-\ln \zeta(s)$ the only known series with primes and nontrivial closed form?

Published on 30 Aug 2016 - 21:55

score 211 · Answer 4 · 2016-08-31 07:35:33

211

Views

Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.

Published on 31 Aug 2016 - 7:35

score 184 · Answer 5 · 2016-08-31 11:01:51

184

Views

Interesting connection between polylogarithms and polygamma functions.

Published on 31 Aug 2016 - 11:01

score 319 · Answer 6 · 2016-08-31 20:00:42

319

Views

Is a closed form version of the Look and Say sequence useful?

Published on 31 Aug 2016 - 20:00

score 223 · Answer 7 · 2016-09-02 05:19:31

223

Views

Evaluate the integral $\int_{\large \frac13}^3\frac{\sin^{-1}\frac x{\sqrt{1+x^2}}}xdx$

Published on 02 Sep 2016 - 5:19

score 1.3k · Answer 8 · 2016-09-03 17:18:25

1.3k

Views

Improper Integral $\int_0^\infty\left(\frac{\tanh(x)}{x^3}-\frac1{x^2\cosh^2(x)}\right)dx = \frac{7\zeta(3)}{\pi^2} $

Published on 03 Sep 2016 - 17:18

score 411 · Answer 9 · 2016-09-04 06:37:29

411

Views

Improper Integral $\int_0^\infty\tan\left(\frac x{\sqrt{x^3+x^2}}\right)\frac{\ln(1+\sqrt x)}xdx$

Published on 04 Sep 2016 - 6:37

score 168 · Answer 10 · 2016-09-05 14:03:38

168

Views

Generating function of squares of generalized harmonic numbers

Published on 05 Sep 2016 - 14:03

score 263 · Answer 11 · 2016-09-08 14:44:04

263

Views

Prime Telescoping Series

Published on 08 Sep 2016 - 14:44

score 89 · Answer 12 · 2016-09-08 15:49:42

89

Views

A family of generating functions related to generalized harmonic numbers and power functions.

Published on 08 Sep 2016 - 15:49

score 831 · Answer 13 · 2016-09-10 01:20:46

831

Views

Improper Integral $\int_0^\infty\log(x)e^{-x^2}dx$

Published on 10 Sep 2016 - 1:20

score 64 · Answer 14 · 2016-09-11 08:33:19

64

Views

A Proof using Telescopic Sum: $a_1=3,\,2a_n = 1+a_{n-1};\;n\ge 2.$

Published on 11 Sep 2016 - 8:33

score 334 · Answer 15 · 2026-03-31 06:02:04

334

Views

Calculus - Finding limit (NOT L'Hopital's Rule): $\lim_{x \to 1^-}\frac{x^2+x+\sin({\pi\over 2}x)-3}{x-1}$

Published on 31 Mar 2026 - 6:02

List Question

Alternative form to express the second derivative of $\zeta (2) $

Finding a closed form for binomial coefficient summation

Is $\sum_{n=1}^\infty \ln \left(1-\frac{1}{p_n^s} \right)=-\ln \zeta(s)$ the only known series with primes and nontrivial closed form?

Show that $e^{-\beta} = \frac{1}{\sqrt{\pi}} \int_{0}^{\infty} \frac{e^{-u}}{\sqrt{u}} e^{-\beta^2 / 4u} du$.

Interesting connection between polylogarithms and polygamma functions.

Is a closed form version of the Look and Say sequence useful?

Evaluate the integral $\int_{\large \frac13}^3\frac{\sin^{-1}\frac x{\sqrt{1+x^2}}}xdx$

Improper Integral $\int_0^\infty\left(\frac{\tanh(x)}{x^3}-\frac1{x^2\cosh^2(x)}\right)dx = \frac{7\zeta(3)}{\pi^2} $

Improper Integral $\int_0^\infty\tan\left(\frac x{\sqrt{x^3+x^2}}\right)\frac{\ln(1+\sqrt x)}xdx$

Generating function of squares of generalized harmonic numbers

Prime Telescoping Series

A family of generating functions related to generalized harmonic numbers and power functions.

Improper Integral $\int_0^\infty\log(x)e^{-x^2}dx$

A Proof using Telescopic Sum: $a_1=3,\,2a_n = 1+a_{n-1};\;n\ge 2.$

Calculus - Finding limit (NOT L'Hopital's Rule): $\lim_{x \to 1^-}\frac{x^2+x+\sin({\pi\over 2}x)-3}{x-1}$

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