Compute all the unnormalized associated Legendre functions.
call PLegendreA (p
, lmax
, z
, csphase
)
p
: output, real*8, 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+1
, which can be calculated by a call to PlmIndex
.
lmax
: input, integer
: The maximum degree of the associated Legendre functions to be computed.
z
: input, real*8
: The argument of the associated Legendre functions.
csphase
: input, 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+1
and can be computed by a call to PlmIndex
. 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
, plmindex