Question

Why do these two integrals use roots of reciprocal polynomials?

score 442 · Answer 1 · 2026-03-26 19:17:16

442

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Why do these two integrals use roots of reciprocal polynomials?

Published on 26 Mar 2026 - 19:17

score 183 · Answer 2 · 2026-03-30 14:18:26

183

Views

Closed form solution for time-dependent harmonic oscillator

Published on 30 Mar 2026 - 14:18

score 120 · Answer 3 · 2016-12-04 16:21:16

120

Views

Closed form of recursively defined sequence

Published on 04 Dec 2016 - 16:21

score 146 · Answer 4 · 2016-12-07 04:09:12

146

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closed-form of an integral that may relate to the elliptic integral

Published on 07 Dec 2016 - 4:09

score 34 · Answer 5 · 2026-03-26 14:23:05

34

Views

On the integral representation of the function $b(s)$ defining $b(n)=\operatorname{Bernoulli}_{2n}$, and Riemann's trick

Published on 26 Mar 2026 - 14:23

score 475 · Answer 6 · 2026-03-26 19:20:12

475

Views

How to generalize Reshetnikov's $\arg\,B\left(\frac{-5+8\,\sqrt{-11}}{27};\,\frac12,\frac13\right)=\frac\pi3$?

Published on 26 Mar 2026 - 19:20

score 208 · Answer 7 · 2026-03-29 01:35:38

208

Views

Is there a general form for $a_n=\sqrt{2+a_{n-1}}$?

Published on 29 Mar 2026 - 1:35

score 60 · Answer 8 · 2016-12-11 20:00:31

60

Views

strategies to find explicit formulae for series

Published on 11 Dec 2016 - 20:00

score 168 · Answer 9 · 2026-03-29 09:11:39

168

Views

Closed form and/or approximation for $f_n=\sum\limits_{i=1}^{n-1}\binom{n}{i}\cdot i\cdot \log(i)$

Published on 29 Mar 2026 - 9:11

score 1.4k · Answer 10 · 2016-12-15 21:48:59

1.4k

Views

How to find closed form formula for sequences defined by $a_n = ra_{n-1} + d$

Published on 15 Dec 2016 - 21:48

score 188 · Answer 11 · 2016-12-16 09:40:12

188

Views

Generating function of exponential integrals

Published on 16 Dec 2016 - 9:40

score 134 · Answer 12 · 2026-03-29 17:11:47

134

Views

Is there a known transformation between $_2F_1\big(\tfrac12,\tfrac12;1;z\big)$ and $_2F_1\big(\tfrac12,\tfrac12;1;z^2\big)$?

Published on 29 Mar 2026 - 17:11

score 318 · Answer 13 · 2016-12-17 19:01:01

318

Views

Math competition problem, prove that $\int_{-\infty}^\infty e^{-\pi x^2 \left(\frac{\alpha +x}{\beta +x}\right)^2}dx=1~$ for $~0<\beta<\alpha$.

Published on 17 Dec 2016 - 19:01

score 254 · Answer 14 · 2026-03-29 18:36:24

254

Views

Prove that $\ln{\left({A^6\sqrt{\pi}\over 2^{7\over6}e}\right)}=\sum\limits_{n=1}^{\infty}{(-1)^{n+1}\over n(n+1)}\eta(n)$

Published on 29 Mar 2026 - 18:36

score 69 · Answer 15 · 2026-03-28 01:05:57

69

Views

Finding closed form for recurrent function with 2 variables

Published on 28 Mar 2026 - 1:05

List Question

Why do these two integrals use roots of reciprocal polynomials?

Closed form solution for time-dependent harmonic oscillator

Closed form of recursively defined sequence

closed-form of an integral that may relate to the elliptic integral

On the integral representation of the function $b(s)$ defining $b(n)=\operatorname{Bernoulli}_{2n}$, and Riemann's trick

How to generalize Reshetnikov's $\arg\,B\left(\frac{-5+8\,\sqrt{-11}}{27};\,\frac12,\frac13\right)=\frac\pi3$?

Is there a general form for $a_n=\sqrt{2+a_{n-1}}$?

strategies to find explicit formulae for series

Closed form and/or approximation for $f_n=\sum\limits_{i=1}^{n-1}\binom{n}{i}\cdot i\cdot \log(i)$

How to find closed form formula for sequences defined by $a_n = ra_{n-1} + d$

Generating function of exponential integrals

Is there a known transformation between $_2F_1\big(\tfrac12,\tfrac12;1;z\big)$ and $_2F_1\big(\tfrac12,\tfrac12;1;z^2\big)$?

Math competition problem, prove that $\int_{-\infty}^\infty e^{-\pi x^2 \left(\frac{\alpha +x}{\beta +x}\right)^2}dx=1~$ for $~0<\beta<\alpha$.

Prove that $\ln{\left({A^6\sqrt{\pi}\over 2^{7\over6}e}\right)}=\sum\limits_{n=1}^{\infty}{(-1)^{n+1}\over n(n+1)}\eta(n)$

Finding closed form for recurrent function with 2 variables

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