Question

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

score 48 · Answer 1 · 2021-09-06 09:07:41

48

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 06 Sep 2021 - 9:07

score 107 · Answer 2 · 2026-03-26 13:51:27

107

Views

How could a "fan-shaped" transformation of the angles be mathematically described?

Published on 26 Mar 2026 - 13:51

score 142 · Answer 3 · 2021-09-07 17:11:39

142

Views

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

Published on 07 Sep 2021 - 17:11

score 34 · Answer 4 · 2021-09-07 21:51:23

34

Views

Taylor coefficients of certain "deformed" Bessel functions

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score 44 · Answer 5 · 2026-03-26 09:25:36

44

Views

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score 57 · Answer 6 · 2021-09-12 07:24:43

57

Views

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score 2.4k · Answer 7 · 2021-09-13 15:20:29

2.4k

Views

How to convert $x^2-y^2-z^2 = 1$ to spherical equation?

Published on 13 Sep 2021 - 15:20

score 1.6k · Answer 8 · 2026-03-26 13:48:05

1.6k

Views

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score 425 · Answer 9 · 2026-03-13 16:31:51

425

Views

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score 66 · Answer 10 · 2021-09-17 04:47:50

66

Views

Triple Intergal in spherical coordinates

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score 649 · Answer 11 · 2021-09-17 11:47:55

649

Views

Viewing Direction as 3D Cartesian Unit Vector

Published on 17 Sep 2021 - 11:47

score 56 · Answer 12 · 2021-09-21 21:09:39

56

Views

Closed-form formula for $u(t):= \mathbb E[h(X_1)h(tX_1+(1-t^2)^{1/2} X_2)]$, where $(X_1,X_2,\ldots,X_d)$ is uniform on sphere and $h(x):=(x+c)^k$

Published on 21 Sep 2021 - 21:09

score 62 · Answer 13 · 2021-09-28 17:22:26

62

Views

Analytic formula for $\lim_{n \to \infty}E[g(z_1)g(z_2)]$ where $(z_1,\ldots,z_n)$ is uniform on unit-sphere in $R^n$ and $g:R \to R$ is continuous

Published on 28 Sep 2021 - 17:22

score 261 · Answer 14 · 2026-03-29 01:35:42

261

Views

Distance metric between two points on a sphere, Haversine formula versus 3D Cartesian surface distance

Published on 29 Mar 2026 - 1:35

score 57 · Answer 15 · 2021-10-08 00:14:46

57

Views

Integral in spherical coordinates.

Published on 08 Oct 2021 - 0:14

List Question

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 could a "fan-shaped" transformation of the angles be mathematically described?

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

Is there any spherical rectangle that is closed under intersection/complement?

Question regarding finding a basis vector

How to convert $x^2-y^2-z^2 = 1$ to spherical equation?

Divergence of a radial vector field

Pyramid - Cartesian Space xyz

Triple Intergal in spherical coordinates

Viewing Direction as 3D Cartesian Unit Vector

Closed-form formula for $u(t):= \mathbb E[h(X_1)h(tX_1+(1-t^2)^{1/2} X_2)]$, where $(X_1,X_2,\ldots,X_d)$ is uniform on sphere and $h(x):=(x+c)^k$

Analytic formula for $\lim_{n \to \infty}E[g(z_1)g(z_2)]$ where $(z_1,\ldots,z_n)$ is uniform on unit-sphere in $R^n$ and $g:R \to R$ is continuous

Distance metric between two points on a sphere, Haversine formula versus 3D Cartesian surface distance

Integral in spherical coordinates.

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