Question

A closed form for the sum $\sum_{k=0}^{\infty}\frac{\Gamma{(a k)}}{\Gamma{(b k)}}{\lambda}^{-k}$ where $0<a<b$?

score 43 · Answer 1 · 2023-05-07 20:46:44

43

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A closed form for the sum $\sum_{k=0}^{\infty}\frac{\Gamma{(a k)}}{\Gamma{(b k)}}{\lambda}^{-k}$ where $0<a<b$?

Published on 07 May 2023 - 20:46

score 74 · Answer 2 · 2026-04-01 10:43:12

74

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A question regarding the construction of binary sequences

Published on 01 Apr 2026 - 10:43

score 38 · Answer 3 · 2023-05-08 07:31:22

Closed form for $\sum_k\left(\begin{array}{l}n \\ k\end{array}\right)\left(\begin{array}{c}2 k \\ k\end{array}\right)\left(-\frac{1}{2}\right)^k$

score 58 · Answer 4 · 2023-05-09 16:02:40

58

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Closed form for $\int_0^{\pi/2}(\cos^2{\theta})^{1/n}d\theta$

Published on 09 May 2023 - 16:02

score 60 · Answer 5 · 2023-05-10 08:49:54

60

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Electron Vertex in Fourth Order

Published on 10 May 2023 - 8:49

score 402 · Answer 6 · 2026-03-30 03:37:52

402

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Probability of winning a coin toss game

Published on 30 Mar 2026 - 3:37

score 86 · Answer 7 · 2023-05-14 14:37:16

86

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Closed form for a family of integrals of the form $\int_{0}^{\infty}\Phi(x)x^{m}\cosh(x)dx$ and $\int_{0}^{\infty}\Phi(x)x^{m}\sinh(x)dx$

Published on 14 May 2023 - 14:37

score 89 · Answer 8 · 2023-05-18 10:18:08

89

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Closed-form expression for sum of Modulo Arithmetic Progression

Published on 18 May 2023 - 10:18

score 188 · Answer 9 · 2023-05-18 18:58:34

188

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Does this series have a closed form? If so, what is it?

Published on 18 May 2023 - 18:58

score 158 · Answer 10 · 2023-05-20 03:33:44

158

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Is every real number representable as an exact expression?

Published on 20 May 2023 - 3:33

score 97 · Answer 11 · 2026-02-24 05:18:32

97

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Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Published on 24 Feb 2026 - 5:18

score 64 · Answer 12 · 2026-03-30 12:23:43

64

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Integral of the product of Hankel function and exponential

Published on 30 Mar 2026 - 12:23

score 262 · Answer 13 · 2026-03-25 21:51:09

262

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Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Published on 25 Mar 2026 - 21:51

score 52 · Answer 14 · 2023-06-02 09:52:55

52

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Closed form for $\int_{0}^{1}((\frac{2\arctan(x)}{x}-\frac{3}{2}x^{\frac{1}{2}})((\frac{6}{5}-x^{\frac{4}{5}}-\frac{1}{10})^{\frac{6}{5}}))^{1/2}dx=?$

Published on 02 Jun 2023 - 9:52

score 197 · Answer 15 · 2026-03-28 10:17:38

197

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Zeros of a complex function on the unit circle

Published on 28 Mar 2026 - 10:17

List Question

A closed form for the sum $\sum_{k=0}^{\infty}\frac{\Gamma{(a k)}}{\Gamma{(b k)}}{\lambda}^{-k}$ where $0<a<b$?

A question regarding the construction of binary sequences

Closed form for $\sum_k\left(\begin{array}{l}n \\ k\end{array}\right)\left(\begin{array}{c}2 k \\ k\end{array}\right)\left(-\frac{1}{2}\right)^k$

Closed form for $\int_0^{\pi/2}(\cos^2{\theta})^{1/n}d\theta$

Electron Vertex in Fourth Order

Probability of winning a coin toss game

Closed form for a family of integrals of the form $\int_{0}^{\infty}\Phi(x)x^{m}\cosh(x)dx$ and $\int_{0}^{\infty}\Phi(x)x^{m}\sinh(x)dx$

Closed-form expression for sum of Modulo Arithmetic Progression

Does this series have a closed form? If so, what is it?

Is every real number representable as an exact expression?

Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Integral of the product of Hankel function and exponential

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Closed form for $\int_{0}^{1}((\frac{2\arctan(x)}{x}-\frac{3}{2}x^{\frac{1}{2}})((\frac{6}{5}-x^{\frac{4}{5}}-\frac{1}{10})^{\frac{6}{5}}))^{1/2}dx=?$

Zeros of a complex function on the unit circle

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