Question

Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$

score 877 · Answer 1 · 2014-06-18 04:44:27

877

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Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$

Published on 18 Jun 2014 - 4:44

score 306 · Answer 2 · 2014-06-19 14:41:01

306

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What is the sum of Psi/Digamma-function of consecutive arguments? Is there a closed form?

Published on 19 Jun 2014 - 14:41

score 1.1k · Answer 3 · 2026-03-25 18:49:06

1.1k

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Is there a closed form expression for the sum of all the proper divisors of an integer?

Published on 25 Mar 2026 - 18:49

score 1.1k · Answer 4 · 2014-06-22 01:02:36

1.1k

Views

Approximate value of a slowly-converging sum of $\sum|\sin n|^n/n$

Published on 22 Jun 2014 - 1:02

score 498 · Answer 5 · 2026-03-25 22:26:54

498

Views

Proving that $\int_0^\infty\Big(\sqrt[n]{1+x^n}-x\Big)dx~=~\frac12\cdot{-1/n\choose+1/n}^{-1}$

Published on 25 Mar 2026 - 22:26

score 85 · Answer 6 · 2014-06-25 13:50:38

85

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Does $\sum_{i=1}^{k-1}\lceil \log_2\frac{N}{i}\rceil$ have a closed form?

Published on 25 Jun 2014 - 13:50

score 615 · Answer 7 · 2014-06-27 22:49:26

615

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Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

Published on 27 Jun 2014 - 22:49

score 167 · Answer 8 · 2014-06-29 14:09:07

167

Views

Closed form for $f(x)=\int_{0}^{+\infty}e^{it^{x}}dt$?

Published on 29 Jun 2014 - 14:09

score 277 · Answer 9 · 2014-07-02 20:51:24

277

Views

Is there a closed form solution to $e^{-x/b}(a+x) = e^{x/b}(a-x)$?

Published on 02 Jul 2014 - 20:51

score 177 · Answer 10 · 2014-07-03 11:48:31

177

Views

Evaluate $\int_0^\infty x^{\lambda-1} \exp\left(-ax-b\sqrt x-\frac{c}{\sqrt x} - \frac{d}{x}\right) \: dx$

Published on 03 Jul 2014 - 11:48

score 94 · Answer 11 · 2014-07-03 17:33:00

94

Views

closed form expression for an infinite sum

Published on 03 Jul 2014 - 17:33

score 219 · Answer 12 · 2014-07-05 07:39:13

219

Views

Closed form of $\sum_{k=0}^nk\binom{k}{3}\binom{2n}{k}$

Published on 05 Jul 2014 - 7:39

score 147 · Answer 13 · 2026-03-25 10:15:42

147

Views

closed-form term for this sum:

Published on 25 Mar 2026 - 10:15

score 62 · Answer 14 · 2014-07-07 23:51:44

62

Views

closed form for $\int_0^1x^{a+1}(1-x^2)^bJ_a(cx)dx$

Published on 07 Jul 2014 - 23:51

score 223 · Answer 15 · 2014-07-10 07:22:41

223

Views

Closed-form term for $\sum_{i=1}^{\infty} i q^i$

Published on 10 Jul 2014 - 7:22

List Question

Evaluate $\int_{0}^1 \prod_{k=2}^n \lfloor kx \rfloor dx$

What is the sum of Psi/Digamma-function of consecutive arguments? Is there a closed form?

Is there a closed form expression for the sum of all the proper divisors of an integer?

Approximate value of a slowly-converging sum of $\sum|\sin n|^n/n$

Proving that $\int_0^\infty\Big(\sqrt[n]{1+x^n}-x\Big)dx~=~\frac12\cdot{-1/n\choose+1/n}^{-1}$

Does $\sum_{i=1}^{k-1}\lceil \log_2\frac{N}{i}\rceil$ have a closed form?

Help with logarithmic definite integral: $\int_0^1\frac{1}{x}\ln{(x)}\ln^3{(1-x)}\, dx$

Closed form for $f(x)=\int_{0}^{+\infty}e^{it^{x}}dt$?

Is there a closed form solution to $e^{-x/b}(a+x) = e^{x/b}(a-x)$?

Evaluate $\int_0^\infty x^{\lambda-1} \exp\left(-ax-b\sqrt x-\frac{c}{\sqrt x} - \frac{d}{x}\right) \: dx$

closed form expression for an infinite sum

Closed form of $\sum_{k=0}^nk\binom{k}{3}\binom{2n}{k}$

closed-form term for this sum:

closed form for $\int_0^1x^{a+1}(1-x^2)^bJ_a(cx)dx$

Closed-form term for $\sum_{i=1}^{\infty} i q^i$

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