# sphericalHarmonics: Compute spherical harmonic values at given points on the... In rcosmo: Cosmic Microwave Background Data Analysis

## Description

The function `sphericalHarmonics` computes the spherical harmonic values for the given 3D Cartesian coordinates.

## Usage

 `1` ```sphericalHarmonics(L, m, xyz) ```

## Arguments

 `L` The degree of spherical harmonic (L=0,1,2,...) `m` The order number of the degree-L spherical harmonic (m=-L,-L+1,...,L-1,L) `xyz` Dataframe for given points in 3D cartesian coordinates

## Value

values of spherical harmonics

## References

See https://en.wikipedia.org/wiki/Table_of_spherical_harmonics

It uses equation (7) in Hesse, K., Sloan, I. H., & Womersley, R. S. (2010). Numerical integration on the sphere. In Handbook of Geomathematics (pp. 1185-1219). Springer Berlin Heidelberg,

but instead of the order k=1,...,2L+1 in the book we use m=k-L-1.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Calculate spherical harmonic value at ## the point (0,1,0) with L=5, m=2 point<-data.frame(x=0,y=1,z=0) sphericalHarmonics(5,2,point) ## Calculate spherical harmonic values at ## the point (1,0,0), (0,1,0), (0,0,1) with L=5, m=2 points<-data.frame(diag(3)) sphericalHarmonics(5,2,points) ```

rcosmo documentation built on Feb. 14, 2020, 5:06 p.m.