Question

Verification of Sum without closed-form expression

score 87 · Answer 1 · 2026-04-07 23:39:55

87

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Verification of Sum without closed-form expression

Published on 07 Apr 2026 - 23:39

score 1.3k · Answer 2 · 2017-08-12 19:50:49

1.3k

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Closed Form for this Taylor Series?

Published on 12 Aug 2017 - 19:50

score 39 · Answer 3 · 2017-08-13 13:33:08

39

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Closed form of $\int_0^x \frac{d y}{\sqrt{y^2+n^2}}\ln\frac{\sqrt{y^2+n^2}+y}{\sqrt{y^2+n^2}-y}$

Published on 13 Aug 2017 - 13:33

score 93 · Answer 4 · 2017-08-14 19:09:37

93

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The sequence A126022 : $a_{n+1} = a_n + \lfloor a^{-1}(n+1) \rfloor $

Published on 14 Aug 2017 - 19:09

score 130 · Answer 5 · 2017-08-15 14:50:03

130

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Asymptotics for the sequence A094589

Published on 15 Aug 2017 - 14:50

score 1k · Answer 6 · 2026-04-07 19:35:31

1k

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Prove $\int_0^1 \frac{4\cos^{-1}x}{\sqrt{2x-x^2}}\,dx=\frac{8}{9\sqrt{\pi}}\left(9\Gamma(3/4)^2{}_4F_3(\cdots)+\Gamma(5/4)^2{}_4F_3(\cdots)\right)$

Published on 07 Apr 2026 - 19:35

score 537 · Answer 7 · 2017-08-17 10:42:48

537

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Closed form for a series of functions

Published on 17 Aug 2017 - 10:42

score 1.3k · Answer 8 · 2026-03-30 07:09:27

1.3k

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A closed form of $\sum_{n=1}^\infty\left[ H_n^2-\left(\ln n+\gamma+\frac1{2n} \right)^2\right]$

Published on 30 Mar 2026 - 7:09

score 399 · Answer 9 · 2017-08-21 13:28:56

399

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Closed-forms of definite integrals

Published on 21 Aug 2017 - 13:28

score 730 · Answer 10 · 2017-08-21 21:36:38

730

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Is there a closed form for $\sum_{n=0}^{\infty}{2^{n+1}\over {2n \choose n}}\cdot\left({2n-1\over 2n+1}\right)^2?$

Published on 21 Aug 2017 - 21:36

score 322 · Answer 11 · 2017-08-22 05:22:58

322

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Evaluate$ \int _0^{\infty} \frac{\operatorname{sech}^{k}(x)}{\cosh(2\pi/k)-\cos(2x)}\,dx $ for $k=1,2$

Published on 22 Aug 2017 - 5:22

score 56 · Answer 12 · 2026-03-26 08:03:17

56

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Closed form or asymptotic expansion for the summation relating to the elliptic integral

Published on 26 Mar 2026 - 8:03

score 226 · Answer 13 · 2026-04-08 16:09:31

226

Views

Closed-form for Floor Sum 3 - With knowledge of inner expression

Published on 08 Apr 2026 - 16:09

score 134 · Answer 14 · 2026-03-29 14:02:42

134

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Infinite trigonometry Summation: $ \sum_{k=1}^\infty \left( \cos \frac{\pi}{2k}-\cos \frac{\pi}{2(k+2)} \right) $

Published on 29 Mar 2026 - 14:02

score 772 · Answer 15 · 2026-02-23 05:14:25

772

Views

asymptotic expansion of a series related to $\cosh(x)$

Published on 23 Feb 2026 - 5:14

List Question

Verification of Sum without closed-form expression

Closed Form for this Taylor Series?

Closed form of $\int_0^x \frac{d y}{\sqrt{y^2+n^2}}\ln\frac{\sqrt{y^2+n^2}+y}{\sqrt{y^2+n^2}-y}$

The sequence A126022 : $a_{n+1} = a_n + \lfloor a^{-1}(n+1) \rfloor $

Asymptotics for the sequence A094589

Prove $\int_0^1 \frac{4\cos^{-1}x}{\sqrt{2x-x^2}}\,dx=\frac{8}{9\sqrt{\pi}}\left(9\Gamma(3/4)^2{}_4F_3(\cdots)+\Gamma(5/4)^2{}_4F_3(\cdots)\right)$

Closed form for a series of functions

A closed form of $\sum_{n=1}^\infty\left[ H_n^2-\left(\ln n+\gamma+\frac1{2n} \right)^2\right]$

Closed-forms of definite integrals

Is there a closed form for $\sum_{n=0}^{\infty}{2^{n+1}\over {2n \choose n}}\cdot\left({2n-1\over 2n+1}\right)^2?$

Evaluate$ \int _0^{\infty} \frac{\operatorname{sech}^{k}(x)}{\cosh(2\pi/k)-\cos(2x)}\,dx $ for $k=1,2$

Closed form or asymptotic expansion for the summation relating to the elliptic integral

Closed-form for Floor Sum 3 - With knowledge of inner expression

Infinite trigonometry Summation: $ \sum_{k=1}^\infty \left( \cos \frac{\pi}{2k}-\cos \frac{\pi}{2(k+2)} \right) $

asymptotic expansion of a series related to $\cosh(x)$

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