Compute all the unnormalized associated Legendre functions.

Usage

p = PLegendreA (lmax, z, [csphase])

Returns

p : float, dimension ((lmax+1)*(lmax+2)/2)
An array of unnormalized associated Legendre functions up to degree lmax. The index corresponds to l*(l+1)/2+m.

Parameters

lmax : integer
The maximum degree of the associated Legendre functions to be computed.
z : float
The argument of the associated Legendre functions.
csphase : optional, integer, default = 1
If 1 (default), the Condon-Shortley phase will be excluded. If -1, the Condon-Shortley phase of (-1)^m will be appended to the associated Legendre functions.

Description

PLegendreA will calculate all of the unnormalized associated Legendre functions up to degree lmax for a given argument. These are calculated using a standard three-term recursion formula and hence will overflow for moderate values of l and m. The index of the array corresponding to a given degree l and angular order m corresponds to l*(l+1)/2+m. The integral of the associated Legendre functions over the interval [-1, 1] is 2*(l+m)!/(l-m)!/(2l+1). The default is to exclude the Condon-Shortley phase, but this can be modified by setting the optional argument csphase to -1.

See also

plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1, plschmidt, plschmidt_d1, plmschmidt, plmschmidt_d1, plegendre, plegendre_d1, plegendrea_d1

Tags: python
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