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

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

## 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 Dec. 11, 2021, 9:29 a.m.