legndr - nicolob/pep-full GitHub Wiki

legndr

Type: subroutine

Defined in: legndr.f

Definition: subroutine LEGNDR(z, zz, nzone, ntess, leg, leg1, gleg, gleg1)

Description

legndr  evaluates the legendre polynomials, its
derivatives and also the associated legendre functions
the legendre polynomials are defined as:
pn(z) = (1 / (n!*2**n) ) * (nth derivat of (z*z-1)**n)
and the associated legendre functions as
p(n,h) = ((sqrt(1-z*z))**h) * ph(n) ,
where ph(n) is the  hth derivative of  pn(z)
we can see that for h=0  p(n,0)=pn(z)
the formulae are from  "tables of integrals, series
and products" - gradsteyn & ryzhik,pags 1004-27
$$$$$$$ the factor (-1)**h  for the legendre function used in this
reference has been set = 1 to use the convention of
the smithsonian astr. observatory journal
the formulae for  p'(z)  and  p''(z)  are from "differential
equations with applications", ritger & rose, page 223
evaluation of  p(z)
the first polynomial in the array  leg(n)  is the
second order polynomial, since the first order is not
used in PEP
evaluation of p(n,h)
the order of the legendre functions in the array gleg,
as well as the order of the partials in gleg1, gleg2 is
p(2,1), p(2,2), p(3,1), p(3,2), p(3,3), ....... , p(n,n)

Included Files

None.

Arguments

  • z
  • zz
  • nzone
  • ntess
  • leg
  • leg1
  • gleg
  • gleg1

Calls

  • None detected.

Called By

  • ...

Notes

  • ...
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