Question

Analytic expression for a definite integral containing a trigonometric function and a power of x

score 95 · Answer 1 · 2026-04-15 00:23:44

95

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Analytic expression for a definite integral containing a trigonometric function and a power of x

Published on 15 Apr 2026 - 0:23

score 278 · Answer 2 · 2026-04-12 15:59:52

278

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Evaluation of Mellin transform via contours

Published on 12 Apr 2026 - 15:59

score 109 · Answer 3 · 2026-04-16 07:41:21

109

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Inverse of $x(e^{-x} - 1)$ for $x \geq 0$?

Published on 16 Apr 2026 - 7:41

score 309 · Answer 4 · 2026-04-15 16:18:18

309

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Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

Published on 15 Apr 2026 - 16:18

score 160 · Answer 5 · 2026-04-11 08:21:06

160

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When is a product of two two-parameter Mittag-Leffler functions a Mittag-Leffler function?

Published on 11 Apr 2026 - 8:21

score 104 · Answer 6 · 2026-04-13 21:04:20

104

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Trigonometric wizardry with the Gamma function

Published on 13 Apr 2026 - 21:04

score 150 · Answer 7 · 2026-04-10 10:24:55

150

Views

Integral Involving Bessel function and trigonometric function

Published on 10 Apr 2026 - 10:24

score 95 · Answer 8 · 2026-04-14 14:49:16

95

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Joint density function of $(X^\top u,X^\top v)$, where $u$ and $v$ are unit-vectors in $R^d$ and $X$ is uniform on the unit sphere in $R^d$.

Published on 14 Apr 2026 - 14:49

score 225 · Answer 9 · 2026-04-12 02:08:19

225

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ODE: $y''y+ax+by+c=0,y=k\pm\sqrt2\int\sqrt{a\int\ln(y)dx-(ax+c)\,\ln(y)-by+K}dx,\int\frac{dy}{\sqrt{K-(ax+c)\,\ln(y)+a\int\ln(y)dx-by}}=k\pm\sqrt2x$

Published on 12 Apr 2026 - 2:08

score 121 · Answer 10 · 2026-04-15 23:23:20

121

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Analytic formula for integral $\int_{-\pi}^\pi (\cos\theta)^n(t\cos\theta + \sqrt{1-t^2}\sin\theta)^n\mathrm{d}\theta $ in terms of special functions

Published on 15 Apr 2026 - 23:23

score 68 · Answer 11 · 2026-04-13 02:54:33

68

Views

Simplify via special functions, a certain sum involving binomial coefficients

Published on 13 Apr 2026 - 2:54

score 51 · Answer 12 · 2026-04-15 20:31:34

51

Views

For $h(t) \equiv e^{ct}$, express $\int_{-\pi}^\pi h(\cos x)h(t\cos x + (1-t^2)^{1/2}\sin x)dx$ in terms of special polynomials / functions

Published on 15 Apr 2026 - 20:31

score 145 · Answer 13 · 2026-04-17 13:13:18

145

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How to compute $\frac{1}{2\pi}\int_{-\pi}^\pi (\cos y + x)^{2k}dy$ and similar integrals

Published on 17 Apr 2026 - 13:13

score 37 · Answer 14 · 2026-04-16 00:31:27

37

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Taylor coefficients of certain "deformed" Bessel functions

Published on 16 Apr 2026 - 0:31

score 197 · Answer 15 · 2026-04-10 23:01:11

197

Views

Asymptotics of Bessel function of first kind

Published on 10 Apr 2026 - 23:01

List Question

Analytic expression for a definite integral containing a trigonometric function and a power of x

Evaluation of Mellin transform via contours

Inverse of $x(e^{-x} - 1)$ for $x \geq 0$?

Staver's identity relating $\sum_{k=1}^{n}\binom{2k}{k}\frac{1}{k}$ and $\sum_{k=1}^{n}\left(k\binom{n}{k}\right)^{-2}$

When is a product of two two-parameter Mittag-Leffler functions a Mittag-Leffler function?

Trigonometric wizardry with the Gamma function

Integral Involving Bessel function and trigonometric function

Joint density function of $(X^\top u,X^\top v)$, where $u$ and $v$ are unit-vectors in $R^d$ and $X$ is uniform on the unit sphere in $R^d$.

ODE: $y''y+ax+by+c=0,y=k\pm\sqrt2\int\sqrt{a\int\ln(y)dx-(ax+c)\,\ln(y)-by+K}dx,\int\frac{dy}{\sqrt{K-(ax+c)\,\ln(y)+a\int\ln(y)dx-by}}=k\pm\sqrt2x$

Analytic formula for integral $\int_{-\pi}^\pi (\cos\theta)^n(t\cos\theta + \sqrt{1-t^2}\sin\theta)^n\mathrm{d}\theta $ in terms of special functions

Simplify via special functions, a certain sum involving binomial coefficients

For $h(t) \equiv e^{ct}$, express $\int_{-\pi}^\pi h(\cos x)h(t\cos x + (1-t^2)^{1/2}\sin x)dx$ in terms of special polynomials / functions

How to compute $\frac{1}{2\pi}\int_{-\pi}^\pi (\cos y + x)^{2k}dy$ and similar integrals

Taylor coefficients of certain "deformed" Bessel functions

Asymptotics of Bessel function of first kind

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