Compute all the unnormalized associated Legendre functions.
p
= PLegendreA (lmax
, z
, [csphase
])
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
.
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.
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.
plbar, plbar_d1, plmbar, plmbar_d1, plon, plon_d1, plmon, plmon_d1, plschmidt, plschmidt_d1, plmschmidt, plmschmidt_d1, plegendre, plegendre_d1, plegendrea_d1