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Legendre functions
spherical harmonics software package, spherical harmonic transform, legendre functions, multitaper spectral analysis, fortran, Python, gravity, magnetic field
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python-legendre-functions.html
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<style> table:nth-of-type(n) { display:table; width:100%; } table:nth-of-type(n) th:nth-of-type(2) { width:75%; } </style>

Convenience functions

Function name Description
legendre Compute all the associated Legendre functions up to a maximum degree and order.
legendre_lm Compute the associated Legendre function for a specific degree l and order m.

4π normalized

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

Orthonormalized

Function 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 normalized

Function 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

Function 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

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