Question

Analytic Form of $\int dx \frac{e^{ - m\sqrt{x^2+b^2}}}{\sqrt{x^2 + b^2}}e^{ikx }$

score 62 · Answer 1 · 2023-08-02 11:40:25

62

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Analytic Form of $\int dx \frac{e^{ - m\sqrt{x^2+b^2}}}{\sqrt{x^2 + b^2}}e^{ikx }$

Published on 02 Aug 2023 - 11:40

score 157 · Answer 2 · 2026-03-25 14:27:03

157

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How to finish the integral $\int_{0}^{\infty}\frac{\sin(x)}{\sinh(x)}\,dx$

Published on 25 Mar 2026 - 14:27

score 36 · Answer 3 · 2026-03-25 17:18:21

36

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How to identify a Fox $H$ function from its Mellin transform?

Published on 25 Mar 2026 - 17:18

score 75 · Answer 4 · 2026-03-25 14:26:01

75

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Series expansion for $\displaystyle{\psi(t+2)-\psi\left(\frac{t+3}{2}\right)}$

Published on 25 Mar 2026 - 14:26

score 315 · Answer 5 · 2026-03-30 08:13:49

315

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About the Integral $\int\arcsin\left(\sin^{2}x\right)dx$

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score 117 · Answer 6 · 2026-04-03 11:06:34

117

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Series expansion of the power Reciprocal gamma function

Published on 03 Apr 2026 - 11:06

score 68 · Answer 7 · 2026-03-27 12:14:14

68

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Evaluating $\int\frac{\log(x+a)}{x}\,dx$ in terms of dilogarithms

Published on 27 Mar 2026 - 12:14

score 178 · Answer 8 · 2026-03-29 10:18:32

178

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Closed form for $\sum_{n=1}^\infty\binom{2n}{n}\zeta(m,n+1)x^n$

Published on 29 Mar 2026 - 10:18

score 752 · Answer 9 · 2023-08-16 07:04:20

752

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Asymptotics of $\displaystyle{\sum_{i=0}^n\sqrt{i(n-i)}}$ as $n\to+\infty$

Published on 16 Aug 2023 - 7:04

score 92 · Answer 10 · 2023-08-17 09:20:10

92

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Log-secant integral using exponential generating function $\int_0^{\pi/2}\log^n(\sec^2 x)\ dx$

Published on 17 Aug 2023 - 9:20

score 132 · Answer 11 · 2026-03-26 14:22:41

132

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Does the second positive solution (besides $x = 1$) of the equation $e^{x^2-1}=x^3-x\ln x$ have a closed form?

Published on 26 Mar 2026 - 14:22

score 552 · Answer 12 · 2026-03-26 03:13:25

552

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On the vanishing of the integral $\int^{n+4}_0 dt P_{\ell}\left(1 - \frac{2t}{n+4}\right)(-t+2)_{n+1}$ for $\ell \geq n+2$

Published on 26 Mar 2026 - 3:13

score 323 · Answer 13 · 2026-03-27 06:10:24

323

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What is so special about $\mathbb{Q}(\sqrt{398})$ that it has several good prime generating polynomials?

Published on 27 Mar 2026 - 6:10

score 79 · Answer 14 · 2026-03-28 02:24:24

79

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Is there a form for the inverse of $(1-l x) ^K(1+w x)^{(T-K)}$ in terms of "named" functions (Beta, Gamma, etc)?

Published on 28 Mar 2026 - 2:24

score 161 · Answer 15 · 2026-04-02 17:36:06

161

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On $\zeta(5)$ and the closed form of $\sum_{n= 1}^\infty \frac{1}{n^5(e^{2\pi n}\pm1)}$?

Published on 02 Apr 2026 - 17:36

List Question

Analytic Form of $\int dx \frac{e^{ - m\sqrt{x^2+b^2}}}{\sqrt{x^2 + b^2}}e^{ikx }$

How to finish the integral $\int_{0}^{\infty}\frac{\sin(x)}{\sinh(x)}\,dx$

How to identify a Fox $H$ function from its Mellin transform?

Series expansion for $\displaystyle{\psi(t+2)-\psi\left(\frac{t+3}{2}\right)}$

About the Integral $\int\arcsin\left(\sin^{2}x\right)dx$

Series expansion of the power Reciprocal gamma function

Evaluating $\int\frac{\log(x+a)}{x}\,dx$ in terms of dilogarithms

Closed form for $\sum_{n=1}^\infty\binom{2n}{n}\zeta(m,n+1)x^n$

Asymptotics of $\displaystyle{\sum_{i=0}^n\sqrt{i(n-i)}}$ as $n\to+\infty$

Log-secant integral using exponential generating function $\int_0^{\pi/2}\log^n(\sec^2 x)\ dx$

Does the second positive solution (besides $x = 1$) of the equation $e^{x^2-1}=x^3-x\ln x$ have a closed form?

On the vanishing of the integral $\int^{n+4}_0 dt P_{\ell}\left(1 - \frac{2t}{n+4}\right)(-t+2)_{n+1}$ for $\ell \geq n+2$

What is so special about $\mathbb{Q}(\sqrt{398})$ that it has several good prime generating polynomials?

Is there a form for the inverse of $(1-l x) ^K(1+w x)^{(T-K)}$ in terms of "named" functions (Beta, Gamma, etc)?

On $\zeta(5)$ and the closed form of $\sum_{n= 1}^\infty \frac{1}{n^5(e^{2\pi n}\pm1)}$?

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