Math.SphericalHarmonics.AssociatedLegendre

Provides definitions of associated Legendre functions used in spherical harmonic models.

Documentation

associatedLegendreFunction

Arguments

:: (Floating a, Ord a)

=> Int

Degree n of the desired associated Legendre function.

-> Int

Order m of the desired associated Legendre function.

-> a

-> a

Computes the associated Legendre function of degree n and order m. Note that the resulting function may not be a polynomial, as when m is odd it involves a fractional power of x. As used in the geodesy and magnetics literature, these functions do not include the Condon-Shortley phase.

schmidtSemiNormalizedAssociatedLegendreFunction

Arguments

:: (Floating a, Ord a)

=> Int

Degree n of the desired function.

-> Int

Order m of the desired function.

-> a

-> a

Computes the Schmidt semi-normalized associated Legendre function of degree n and order m. As used in the geodesy and magnetics literature, these functions do not include the Condon-Shortley phase.