Question

Need help with $\int_0^\infty e^{-x}\ln\ln\left(e^x+\sqrt{e^{2x}-1}\right)\,dx$

score 715 · Answer 1 · 2013-11-25 04:00:02

715

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Need help with $\int_0^\infty e^{-x}\ln\ln\left(e^x+\sqrt{e^{2x}-1}\right)\,dx$

Published on 25 Nov 2013 - 4:00

score 1.8k · Answer 2 · 2013-11-25 23:17:19

1.8k

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

Published on 25 Nov 2013 - 23:17

score 710 · Answer 3 · 2013-11-26 20:23:55

710

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Closed form for integral $\int_{0}^{\pi} \left[1 - r \cos\left(\phi\right)\right]^{-n} \phi \,{\rm d}\phi$

Published on 26 Nov 2013 - 20:23

score 207 · Answer 4 · 2013-11-29 01:33:16

How to find algebraic simplification for recurrence relation with closed-form solution, specifically for the Lucas-Lehmer primality test

score 612 · Answer 5 · 2026-03-28 16:44:20

612

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Integral $\int_0^\infty\exp\left(-\sqrt2\,x^2\right)\,\operatorname{erfi}(x)\,\log(x)\,x^3\,dx$

Published on 28 Mar 2026 - 16:44

score 1.7k · Answer 6 · 2026-03-30 05:13:55

1.7k

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Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$

Published on 30 Mar 2026 - 5:13

score 103 · Answer 7 · 2026-04-05 20:14:55

103

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Does $E^2 \; ( E \approx 1.2640847\ldots)$ equal $D \approx 1.5979102\ldots$?

Published on 05 Apr 2026 - 20:14

score 531 · Answer 8 · 2026-03-27 23:48:18

531

Views

Closed form for $\sum_{n=0}^\infty\frac{\operatorname{Li}_{1/2}\left(-2^{-2^{-n}}\right)}{\sqrt{2^n}}$

Published on 27 Mar 2026 - 23:48

score 1.2k · Answer 9 · 2013-12-04 06:56:00

1.2k

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Closed form expression for unusual sum of binomial coefficients

Published on 04 Dec 2013 - 6:56

score 438 · Answer 10 · 2013-12-05 14:15:50

438

Views

Closed form for matrix multiplication

Published on 05 Dec 2013 - 14:15

score 2k · Answer 11 · 2026-03-30 02:11:30

2k

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Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

Published on 30 Mar 2026 - 2:11

score 89 · Answer 12 · 2013-12-14 20:17:30

89

Views

Is "closed-form analysis" a field of study in math?

Published on 14 Dec 2013 - 20:17

score 85 · Answer 13 · 2026-03-27 23:48:49

85

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A closed form for $\sum_{i\cdot j^k=n}(-1)^i$?

Published on 27 Mar 2026 - 23:48

score 999 · Answer 14 · 2013-12-15 13:28:48

999

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Improper Integral $\int\limits_0^\frac{1}{2}x^n\cot(\pi x)\,dx$

Published on 15 Dec 2013 - 13:28

score 345 · Answer 15 · 2013-12-15 21:37:02

345

Views

Analytic solutions to $f(x+y) +h(x+y)= f(x)(g(y)+h(y)) + g(x)(f(y)+h(y)) + h(x)(f(y)+g(y))$?

Published on 15 Dec 2013 - 21:37

List Question

Need help with $\int_0^\infty e^{-x}\ln\ln\left(e^x+\sqrt{e^{2x}-1}\right)\,dx$

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

Closed form for integral $\int_{0}^{\pi} \left[1 - r \cos\left(\phi\right)\right]^{-n} \phi \,{\rm d}\phi$

How to find algebraic simplification for recurrence relation with closed-form solution, specifically for the Lucas-Lehmer primality test

Integral $\int_0^\infty\exp\left(-\sqrt2\,x^2\right)\,\operatorname{erfi}(x)\,\log(x)\,x^3\,dx$

Conjecture $_2F_1\left(\frac14,\frac34;\,\frac23;\,\frac13\right)=\frac1{\sqrt{\sqrt{\frac4{\sqrt{2-\sqrt[3]4}}+\sqrt[3]{4}+4}-\sqrt{2-\sqrt[3]4}-2}}$

Does $E^2 \; ( E \approx 1.2640847\ldots)$ equal $D \approx 1.5979102\ldots$?

Closed form for $\sum_{n=0}^\infty\frac{\operatorname{Li}_{1/2}\left(-2^{-2^{-n}}\right)}{\sqrt{2^n}}$

Closed form expression for unusual sum of binomial coefficients

Closed form for matrix multiplication

Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^22^n}$

Is "closed-form analysis" a field of study in math?

A closed form for $\sum_{i\cdot j^k=n}(-1)^i$?

Improper Integral $\int\limits_0^\frac{1}{2}x^n\cot(\pi x)\,dx$

Analytic solutions to $f(x+y) +h(x+y)= f(x)(g(y)+h(y)) + g(x)(f(y)+h(y)) + h(x)(f(y)+g(y))$?

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