Question

Is there a closed form for $\sum_{k} \frac{1}{\cos (k)}$?

score 137 · Answer 1 · 2026-03-26 11:00:06

137

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Is there a closed form for $\sum_{k} \frac{1}{\cos (k)}$?

Published on 26 Mar 2026 - 11:00

score 263 · Answer 2 · 2017-01-11 19:10:23

263

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Hint needed to figure out sum of the series $x + \frac{x^3}{1\cdot 3} + \frac{x^5}{1\cdot 3\cdot 5}+...$

Published on 11 Jan 2017 - 19:10

score 1.8k · Answer 3 · 2017-01-13 18:44:40

1.8k

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Closed form (or an ODE) for the integral $\int_0^\infty \frac{1+z^2}{1+z^4} \frac{z^p}{1+z^{2p}} dz$

Published on 13 Jan 2017 - 18:44

score 2.5k · Answer 4 · 2017-01-13 21:26:36

2.5k

Views

Closed form of finite sum

Published on 13 Jan 2017 - 21:26

score 43 · Answer 5 · 2026-03-30 11:42:45

43

Views

Are these function cases at all equivalent?

Published on 30 Mar 2026 - 11:42

score 341 · Answer 6 · 2017-01-21 00:44:04

341

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The general term of such a recursion formula

Published on 21 Jan 2017 - 0:44

score 1k · Answer 7 · 2026-03-26 06:34:49

1k

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Interesting closed form for $\int_0^{\frac{\pi}{2}}\frac{1}{\left(\frac{1}{3}+\sin^2{\theta}\right)^{\frac{1}{3}}}\;d\theta$

Published on 26 Mar 2026 - 6:34

score 188 · Answer 8 · 2017-01-21 07:36:47

188

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Does $\int_{0}^{\pi/ n}{\sin^3(x)\over [1+\cos^2(x)]^2}\mathrm dx=F(n)$ have a closed form?

Published on 21 Jan 2017 - 7:36

score 5.2k · Answer 9 · 2017-01-22 11:56:21

5.2k

Views

Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?

Published on 22 Jan 2017 - 11:56

score 196 · Answer 10 · 2017-01-22 15:47:43

196

Views

Find the result of $\sum_{n=1}^{\infty} \sin\left(\frac{1}{2^n}\right)$

Published on 22 Jan 2017 - 15:47

score 129 · Answer 11 · 2017-01-22 20:55:30

129

Views

Exact value of an infinite sum

Published on 22 Jan 2017 - 20:55

score 337 · Answer 12 · 2026-03-26 06:29:44

337

Views

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

Published on 26 Mar 2026 - 6:29

score 262 · Answer 13 · 2026-03-28 21:06:51

262

Views

Closed form for the limit of the iterated sequence $a_{n+1}=\frac{\sqrt{(a_n+b_n)(a_n+c_n)}}{2}$

Published on 28 Mar 2026 - 21:06

score 518 · Answer 14 · 2017-01-24 14:52:40

518

Views

The permutations of the components of the vectors in N-dimensional space are mutually perpendicular

Published on 24 Jan 2017 - 14:52

score 69 · Answer 15 · 2017-01-25 10:35:57

69

Views

Closed form for a hypergeometric sum

Published on 25 Jan 2017 - 10:35

List Question

Is there a closed form for $\sum_{k} \frac{1}{\cos (k)}$?

Hint needed to figure out sum of the series $x + \frac{x^3}{1\cdot 3} + \frac{x^5}{1\cdot 3\cdot 5}+...$

Closed form (or an ODE) for the integral $\int_0^\infty \frac{1+z^2}{1+z^4} \frac{z^p}{1+z^{2p}} dz$

Closed form of finite sum

Are these function cases at all equivalent?

The general term of such a recursion formula

Interesting closed form for $\int_0^{\frac{\pi}{2}}\frac{1}{\left(\frac{1}{3}+\sin^2{\theta}\right)^{\frac{1}{3}}}\;d\theta$

Does $\int_{0}^{\pi/ n}{\sin^3(x)\over [1+\cos^2(x)]^2}\mathrm dx=F(n)$ have a closed form?

Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?

Find the result of $\sum_{n=1}^{\infty} \sin\left(\frac{1}{2^n}\right)$

Exact value of an infinite sum

Prove known closed form for $\int_0^\infty e^{-x}I_0\left(\frac{x}{3}\right)^3\;dx$

Closed form for the limit of the iterated sequence $a_{n+1}=\frac{\sqrt{(a_n+b_n)(a_n+c_n)}}{2}$

The permutations of the components of the vectors in N-dimensional space are mutually perpendicular

Closed form for a hypergeometric sum

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