Question

What about $\int_0^1\int_0^1\int_0^1\frac{1}{1-x\cos\left(\frac{\pi y}{2}\right)\cos\left(\frac{\pi z}{2}\right)}dxdydz\,$?

score 314 · Answer 1 · 2018-04-13 21:48:31

314

Views

What about $\int_0^1\int_0^1\int_0^1\frac{1}{1-x\cos\left(\frac{\pi y}{2}\right)\cos\left(\frac{\pi z}{2}\right)}dxdydz\,$?

Published on 13 Apr 2018 - 21:48

score 53 · Answer 2 · 2018-04-14 08:35:26

53

Views

Closed Form For $n$ Consecutive Summations

Published on 14 Apr 2018 - 8:35

score 1.3k · Answer 3 · 2026-03-22 15:02:00

1.3k

Views

Is it possible to find a closed-form expression for $f(n)$?

Published on 22 Mar 2026 - 15:02

score 57 · Answer 4 · 2018-04-14 19:55:58

57

Views

Closed form of basic looking geometric-like sum

Published on 14 Apr 2018 - 19:55

score 359 · Answer 5 · 2026-03-24 19:08:41

359

Views

Finding the closed-form expression of x

Published on 24 Mar 2026 - 19:08

score 53 · Answer 6 · 2018-04-17 23:06:33

53

Views

$ a(n,K) = \sum_{i = 1}^{n-1} i^K a(i,K) a(n-i,K) $?

Published on 17 Apr 2018 - 23:06

score 47 · Answer 7 · 2018-04-17 23:26:06

47

Views

$ c(n) = \sum_{i = 1}^{n -1} t(i) c(n - i) $?

Published on 17 Apr 2018 - 23:26

score 58 · Answer 8 · 2026-03-25 03:00:46

58

Views

Monotonicity and Bolzano's theorem

Published on 25 Mar 2026 - 3:00

score 182 · Answer 9 · 2018-04-19 20:49:43

182

Views

Closed form for an integral $\int_{0}^{\infty} \frac{dx}{(1+x^2)(5-4\cos(2x))}$

Published on 19 Apr 2018 - 20:49

score 645 · Answer 10 · 2026-03-23 07:45:58

645

Views

Closed form of $\sum_{k=0}^n\binom{2k}{k}(-1/4)^k$

Published on 23 Mar 2026 - 7:45

score 304 · Answer 11 · 2018-04-20 14:57:55

304

Views

How many possibilities are there for at least $k$ consecutive heads to show up out of $n$ tosses?

Published on 20 Apr 2018 - 14:57

score 201 · Answer 12 · 2018-04-20 17:03:16

201

Views

Closed form for $\frac{x}{1+x} +\frac{x^2}{1+x+x^2} +\frac{x^3}{1+x+x^2+x^3}+...$

Published on 20 Apr 2018 - 17:03

score 104 · Answer 13 · 2018-04-21 08:17:43

104

Views

‎Limit of $‎\sum_{n=1}^\infty\frac{x}{\sqrt{n}}-\frac{x}{\sqrt {n+N}}+\sum_{k=1}^N\sum_{n=1}^\infty\frac{1}{\sqrt{n+k+x}}-\frac{1}{\sqrt {n+k}}‎ $‎?

Published on 21 Apr 2018 - 8:17

score 110 · Answer 14 · 2026-03-20 05:53:00

110

Views

Closed form expression for a Gamma-like integral involving a powered Appell hypergeometric function

Published on 20 Mar 2026 - 5:53

score 239 · Answer 15 · 2026-03-22 10:53:50

239

Views

Finding closed form of Frobenius solution

Published on 22 Mar 2026 - 10:53

List Question

What about $\int_0^1\int_0^1\int_0^1\frac{1}{1-x\cos\left(\frac{\pi y}{2}\right)\cos\left(\frac{\pi z}{2}\right)}dxdydz\,$?

Closed Form For $n$ Consecutive Summations

Is it possible to find a closed-form expression for $f(n)$?

Closed form of basic looking geometric-like sum

Finding the closed-form expression of x

$ a(n,K) = \sum_{i = 1}^{n-1} i^K a(i,K) a(n-i,K) $?

$ c(n) = \sum_{i = 1}^{n -1} t(i) c(n - i) $?

Monotonicity and Bolzano's theorem

Closed form for an integral $\int_{0}^{\infty} \frac{dx}{(1+x^2)(5-4\cos(2x))}$

Closed form of $\sum_{k=0}^n\binom{2k}{k}(-1/4)^k$

How many possibilities are there for at least $k$ consecutive heads to show up out of $n$ tosses?

Closed form for $\frac{x}{1+x} +\frac{x^2}{1+x+x^2} +\frac{x^3}{1+x+x^2+x^3}+...$

‎Limit of $‎\sum_{n=1}^\infty\frac{x}{\sqrt{n}}-\frac{x}{\sqrt {n+N}}+\sum_{k=1}^N\sum_{n=1}^\infty\frac{1}{\sqrt{n+k+x}}-\frac{1}{\sqrt {n+k}}‎ $‎?

Closed form expression for a Gamma-like integral involving a powered Appell hypergeometric function

Finding closed form of Frobenius solution

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