legendre-functions.md

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Legendre functions	spherical harmonics software package, spherical harmonic transform, legendre functions, multitaper spectral analysis, fortran, Python, gravity, magnetic field	fortran_sidebar	legendre-functions.html		true	fortran

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$$4 \pi$$ normalized

Routine name	Description
PlmBar	Compute all the 4π-normalized associated Legendre functions.
PlmBar_d1	Compute all the 4π-normalized associated Legendre functions and first derivatives.
PlBar	Compute all the 4π-normalized Legendre polynomials.
PlBar_d1	Compute all the 4π-normalized Legendre Polynomials and first derivatives.

Orthonormalized

Routine name	Description
PlmON	Compute all the orthonormalized associated Legendre functions.
PlmON_d1	Compute all the orthonormalized associated Legendre functions and first derivatives.
PlON	Compute all the orthonormalized Legendre polynomials.
PlON_d1	Compute all the orthonormalized Legendre polynomials and first derivatives.

Schmidt semi-normalized

Routine name	Description
PlmSchmidt	Compute all the Schmidt-normalized associated Legendre functions.
PlmSchmidt_d1	Compute all the Schmidt-normalized associated Legendre functions and first derivatives.
PlSchmidt	Compute all the Schmidt-normalized Legendre polynomials.
PlSchmidt_d1	Compute all the Schmidt-normalized Legendre polynomials and first derivatives.

Unnormalized

Routine name	Description
PLegendreA	Compute all the unnormalized associated Legendre functions.
PLegendreA_d1	Compute all the unnormalized associated Legendre functions and first derivatives.
PLegendre	Compute all the unnormalized Legendre polynomials.
PLegendre_d1	Compute all the unnormalized Legendre polynomials and first derivatives.

Utilities

Routine name	Description
PlmIndex	Compute the index of an array of Legendre functions corresponding to degree l and angular order m.