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PLegendre_d1
Compute all the unnormalized Legendre polynomials and first derivatives.
Usage
call PLegendre_d1 (p
, dp
, lmax
, z
)
Parameters
p
: output, real*8, dimension (lmax
+1)- An array of unnormalized Legendre polynomials up to degree
lmax
. Degreel
corresponds to array indexl
+1. dp
: output, real*8, dimension (lmax
+1)- An array of the first derivatives of the unnormalized Legendre polynomials up to degree
lmax
. Degreel
corresponds to array indexl
+1. lmax
: input, integer- The maximum degree of the Legendre polynomials to be computed.
z
: input, real*8- The argument of the Legendre polynomial.
Description
PLegendre_d1
will calculate all of the unnormalized Legendre polynomials and first derivatives up to degree lmax
for a given argument. These are calculated using a standard three-term recursion formula, and the integral of the Legendre polynomials over the interval [-1, 1] is 2/(2l+1)
. Note that the derivative of the Legendre polynomials is calculated with respect to its arguement z
, and not latitude or colatitude. If z=cos(theta)
, where theta
is the colatitude, then it is only necessary to multiply dp
by -sin(theta)
to obtain the derivative with respect to theta
.
See also
plbar
, plbar_d1
, plmbar
, plmbar_d1
, plon
, plon_d1
, plmon
, plmon_d1
, plschmidt
, plschmidt_d1
, plmschmidt
, plmschmidt_d1
, plegendre
, plegendrea
, plegendrea_d1
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