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DCL:MATH2:SHTLIB: Spherical Harmonic Function: Explanation of Subroutines

4.3.22 SHTFUN

1.

Function

Calculates the associated Legendre function.

2.

Definition

Calculates the associated Legendre function for the specified zonal wavenumber of 0≤m≤M:

P_n^m(sin&phi)      (n =m, m+1,..., M ) (4.35)

(See "Summary" for the definition of the associated Legendre function.)

3.

Call

SHTFUN(MM,JM,M,FUN,WORK)

4.

Explanation of Parameters

MM	(I)	Input parameter. The cut-off wavenumber (M).
JM	(I)	Input parameter. 1/2 of the NS partition number (J)
M	(I)	Input parameter. The zonal wavenumber (m) of the associated Legendre function to calculate.
FUN	(R)	An array of length (2*JM+1)*(MM-M+1) in which is stored. (See Notes for arrangement.)
WORK	(R)	Working area initialized by SHTINT.

5.

Notes

(a)

When FUN(-JM:JM,M:MM) is declared in advance, is stored in FUN(J,N).