Question

Proving there don't exist $F(x), G(x)$ such that $1^{-1}+2^{-1}+3^{-1}+\cdots+n^{-1}={F(n)}/{G(n)}$

score 174 · Answer 1 · 2026-03-29 22:33:50

174

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Proving there don't exist $F(x), G(x)$ such that $1^{-1}+2^{-1}+3^{-1}+\cdots+n^{-1}={F(n)}/{G(n)}$

Published on 29 Mar 2026 - 22:33

score 303 · Answer 2 · 2013-09-03 07:28:28

303

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Closed form of $\sum_{n=1}^\infty \frac{2^{3n}}{2^{4n}+2^{2n}} $?

Published on 03 Sep 2013 - 7:28

score 1k · Answer 3 · 2026-03-29 05:50:19

1k

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Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$

Published on 29 Mar 2026 - 5:50

score 238 · Answer 4 · 2013-09-12 06:45:19

238

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Recursive and closed form solution for choosing $n$ pairs/triplets.. of $kn$ elements.

Published on 12 Sep 2013 - 6:45

score 883 · Answer 5 · 2013-09-12 15:28:39

883

Views

How to find a compact expression for $\sum\limits_{k=1}^n \frac k{(K+1)!}$?

Published on 12 Sep 2013 - 15:28

score 1k · Answer 6 · 2026-03-26 22:16:07

1k

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A closed form for $\int_0^\infty\frac{\sin(x)\ \operatorname{erfi}\left(\sqrt{x}\right)\ e^{-x\sqrt{2}}}{x}dx$

Published on 26 Mar 2026 - 22:16

score 579 · Answer 7 · 2026-03-28 16:45:50

579

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A closed form for $\int_0^\infty e^{-a\,x} \operatorname{erfi}(\sqrt{x})^3\ dx$

Published on 28 Mar 2026 - 16:45

score 566 · Answer 8 · 2026-03-29 05:50:15

566

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Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$

Published on 29 Mar 2026 - 5:50

score 664 · Answer 9 · 2013-09-24 10:46:11

664

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Infinite Series $\sum\limits_{k=1}^{\infty}\frac{k^n}{k!}$

Published on 24 Sep 2013 - 10:46

score 3.2k · Answer 10 · 2013-09-25 17:32:00

3.2k

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How to find a closed form solution to a recurrence of the following form?

Published on 25 Sep 2013 - 17:32

score 266 · Answer 11 · 2013-09-25 20:46:10

266

Views

Number of points in a Bresenham's circle

Published on 25 Sep 2013 - 20:46

score 916 · Answer 12 · 2013-09-26 02:30:18

916

Views

A closed form for $\int_0^\infty\frac{e^{-x}\ J_0(x)\ \sin\left(x\,\sqrt[3]{2}\right)}{x}dx$

Published on 26 Sep 2013 - 2:30

score 3k · Answer 13 · 2026-04-06 15:20:35

3k

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Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$

Published on 06 Apr 2026 - 15:20

score 813 · Answer 14 · 2013-09-26 19:31:46

813

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Integral $\int_0^1\ln\ln\,_3F_2\left(\frac{1}{4},\frac{1}{2},\frac{3}{4};\frac{2}{3},\frac{4}{3};x\right)\,dx$

Published on 26 Sep 2013 - 19:31

score 270 · Answer 15 · 2013-09-27 19:55:42

270

Views

Closed form of $\int_0^2\frac{1}{2+\sqrt{3\,e^x+3\,e^{-x}-2}}dx$

Published on 27 Sep 2013 - 19:55

List Question

Proving there don't exist $F(x), G(x)$ such that $1^{-1}+2^{-1}+3^{-1}+\cdots+n^{-1}={F(n)}/{G(n)}$

Closed form of $\sum_{n=1}^\infty \frac{2^{3n}}{2^{4n}+2^{2n}} $?

Closed form for $\int_{-\infty}^\infty\operatorname{sech}(x)\operatorname{sech}(a\, x)\ dx$

Recursive and closed form solution for choosing $n$ pairs/triplets.. of $kn$ elements.

How to find a compact expression for $\sum\limits_{k=1}^n \frac k{(K+1)!}$?

A closed form for $\int_0^\infty\frac{\sin(x)\ \operatorname{erfi}\left(\sqrt{x}\right)\ e^{-x\sqrt{2}}}{x}dx$

A closed form for $\int_0^\infty e^{-a\,x} \operatorname{erfi}(\sqrt{x})^3\ dx$

Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$

Infinite Series $\sum\limits_{k=1}^{\infty}\frac{k^n}{k!}$

How to find a closed form solution to a recurrence of the following form?

Number of points in a Bresenham's circle

A closed form for $\int_0^\infty\frac{e^{-x}\ J_0(x)\ \sin\left(x\,\sqrt[3]{2}\right)}{x}dx$

Infinite Series $‎\sum\limits_{n=2}^{\infty}\frac{\zeta(n)}{k^n}$

Integral $\int_0^1\ln\ln\,_3F_2\left(\frac{1}{4},\frac{1}{2},\frac{3}{4};\frac{2}{3},\frac{4}{3};x\right)\,dx$

Closed form of $\int_0^2\frac{1}{2+\sqrt{3\,e^x+3\,e^{-x}-2}}dx$

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