Question

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

score 37.6k · Answer 1 · 2013-09-28 00:43:00

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An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

Published on 28 Sep 2013 - 0:43

score 343 · Answer 2 · 2026-03-29 10:15:19

343

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Closed Forms of Certain Zeta constants?

Published on 29 Mar 2026 - 10:15

score 9k · Answer 3 · 2026-03-28 16:44:20

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Integral $\int_0^\infty\left(x+5\,x^5\right)\operatorname{erfc}\left(x+x^5\right)\,dx$

Published on 28 Mar 2026 - 16:44

score 1.6k · Answer 4 · 2013-09-28 23:42:53

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A definite integral $\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx$

Published on 28 Sep 2013 - 23:42

score 1.9k · Answer 5 · 2013-09-29 13:45:36

1.9k

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Integrating $\int_0^ex^{1/x}\ \mathrm dx$

Published on 29 Sep 2013 - 13:45

score 332 · Answer 6 · 2013-09-29 21:59:21

332

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How to solve a recursive equation

Published on 29 Sep 2013 - 21:59

score 136 · Answer 7 · 2026-03-30 04:05:00

136

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closed form $f_n=\sqrt{2f_{n-1}}$ ?

Published on 30 Mar 2026 - 4:05

score 837 · Answer 8 · 2026-03-26 12:08:28

837

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Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor$

Published on 26 Mar 2026 - 12:08

score 457 · Answer 9 · 2013-10-03 06:30:34

457

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Infinite Series $\sum_{k=1}^{\infty}\frac{1}{(mk^2-n)^2}$

Published on 03 Oct 2013 - 6:30

score 83 · Answer 10 · 2026-04-06 15:22:13

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Minimization of $\text{tr} (W^TMW)-\text{tr}(NW)$ subject to $W^TW=I$

Published on 06 Apr 2026 - 15:22

score 587 · Answer 11 · 2013-10-03 20:36:28

587

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A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

Published on 03 Oct 2013 - 20:36

score 486 · Answer 12 · 2013-10-04 05:45:29

486

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Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

Published on 04 Oct 2013 - 5:45

score 1k · Answer 13 · 2013-10-05 00:43:22

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An example of Risch algorithm for integrating $y$, $F(x,y)=0$.

Published on 05 Oct 2013 - 0:43

score 2.5k · Answer 14 · 2026-03-30 03:37:44

2.5k

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A conjectural closed form for $\sum\limits_{n=0}^\infty\frac{n!\,(2n)!}{(3n+2)!}$

Published on 30 Mar 2026 - 3:37

score 1k · Answer 15 · 2013-10-06 10:18:44

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How can we solve $\sin(ax) + \sin(bx) = y$ exactly for constants $a,b > 0$ and $y\in [-2,2]$

Published on 06 Oct 2013 - 10:18

List Question

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

Closed Forms of Certain Zeta constants?

Integral $\int_0^\infty\left(x+5\,x^5\right)\operatorname{erfc}\left(x+x^5\right)\,dx$

A definite integral $\int_0^\infty\frac{2-\cos x}{\left(1+x^4\right)\,\left(5-4\cos x\right)}dx$

Integrating $\int_0^ex^{1/x}\ \mathrm dx$

How to solve a recursive equation

closed form $f_n=\sqrt{2f_{n-1}}$ ?

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{n}\left\lfloor\frac{\log(n)}{\log(2)}\right\rfloor$

Infinite Series $\sum_{k=1}^{\infty}\frac{1}{(mk^2-n)^2}$

Minimization of $\text{tr} (W^TMW)-\text{tr}(NW)$ subject to $W^TW=I$

A closed form for $\int_0^1\frac{\ln(-\ln x)\ \operatorname{li}^2x}{x}dx$

Conjectural closed form for $\int_0^\infty\sqrt[3]z\ \operatorname{Ei}^2(-z)\,dz$

An example of Risch algorithm for integrating $y$, $F(x,y)=0$.

A conjectural closed form for $\sum\limits_{n=0}^\infty\frac{n!\,(2n)!}{(3n+2)!}$

How can we solve $\sin(ax) + \sin(bx) = y$ exactly for constants $a,b > 0$ and $y\in [-2,2]$

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