# Questions tagged [spherical-harmonics]

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### How to solve heat equation in spherical coordinates with finite differences?

I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only. ...
24 views

### Circumferencial waves on a cylinder/sphere

I was wondering how we can introduce $e^{ik.x}$ terms associated with circumferencially propagating waves? In this case $\hat{e}_\theta$ is the direction of wave propagation. However, I was not able ...
2k views

### Fourier Transform of function in Spherical Harmonics

I have a function $f(r,\theta,\phi)$ which I am expressing in terms of spherical harmonics $$f(r,\theta,\phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} g_{l,m}(r) d_{l,m}(\theta,\phi)$$ where $d_{l,m}$...
133 views

### Efficient evaluation of spherical harmonic expansions

Assume I know that I can express an approximation of a function by  \sum_{l=0}^{k}\left( \sqrt{A_l} z_{l,0}^1 L_{l,0}(\theta)+\sqrt{2A_l}\sum_{m=1}^l L_{l,m}(\theta)(z_{l,m}^1 \cos(m\phi)+z_{l,m}^2\...
66 views

### Algorithm for evaluation of spin-weighted spherical harmonics

Is there an algorithm to evaluate spin-weighted spherical harmonics (swSH) at arbitrary points on the sphere? In particular I am looking for, e.g. a recursion relation to evaluate the "spin weighted ...
63 views

### Spherical Gradient along $z$-axis

Let us consider a function $f(r,\theta,\phi)$ that can only be efficiently computed in spherical coordinates. We need its Cartesian gradient. We can implement its analytical spherical derivatives, ...
3k views

### Computing spherical harmonic coefficients using Scipy

The scipy.special.sph_harm function evaluates a spherical harmonic function at a point. Does Scipy provide any functions to compute the spherical harmonic ...
85 views

### Spherical Harmonics: band-limited representations of a vector field on a sphere

I have used pyShtools in the past to expand scalar functions to spherical harmonics and to synthesize band-limited representations of them. However, I am not too sure how to achieve this for a vector ...
460 views

### Discrete Spherical Harmonic Transform from Cartesian grid

I have a grid of data on a 3D Cartesian grid and I would like to find a routine that will allow me to input this data and output a spherical harmonic transform for specific values of radial distances. ...
TLDR: Are these polynomials really harmonic polynomials, and how can I generate them? Long version: I want to describe an electrostatic potential $\Phi(x,y,z)$ over a source-free volume, by using a ...
I am trying to interpolate irregular data $f(\theta, \phi)$ on a sphere and I have so far tried a scipy approach using Kd-Trees and inverse distance weighting, which works ok - however I was wondering ...