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Trailing-Edge - PDP-10 Archives - decuslib20-02 - decus/20-0026/lep.doc
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SUBROUTINE LEP

PURPOSE
   COMPUTE THE VALUES OF THE LEGENDRE POLYNOMIALS P(N,X)
   FOR ARGUMENT VALUE X AND ORDERS 0 UP TO N.

USAGE
   CALL LEP(Y,X,N)

DESCRIPTION OF PARAMETERS
   Y	 - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES
	   OF LEGENDRE POLYNOMIALS OF ORDER 0 UP TO N
	   FOR GIVEN ARGUMENT X.
	   VALUES ARE ORDERED FROM LOW TO HIGH ORDER
   X	 - ARGUMENT OF LEGENDRE POLYNOMIAL
   N	 - ORDER OF LEGENDRE POLYNOMIAL

REMARKS
   N LESS THAN 0 IS TREATED AS IF N WERE 0

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   EVALUATION IS BASED ON THE RECURRENCE EQUATION FOR
   LEGENDRE POLYNOMIALS P(N,X)
   P(N+1,X)=2*X*P(N,X)-P(N-1,X)-(X*P(N,X)-P(N-1,X))/(N+1),
   WHERE THE FIRST TERM IN BRACKETS IS THE ORDER,
   THE SECOND IS THE ARGUMENT.
   STARTING VALUES ARE P(0,X)=1, P(1,X)=X.