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Trailing-Edge - PDP-10 Archives - decuslib20-02 - decus/20-0026/dleps.doc
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SUBROUTINE DLEPS

PURPOSE
   COMPUTES THE VALUE OF AN N-TERM EXPANSION IN LEGENDRE
   POLYNOMIALS WITH COEFFICIENT VECTOR C FOR ARGUMENT VALUE X.

USAGE
   CALL DLEPS(Y,X,C,N)

DESCRIPTION OF PARAMETERS
   Y	 - RESULT VALUE
	   DOUBLE PRECISION VARIABLE
   X	 - ARGUMENT VALUE
	   DOUBLE PRECISION VARIABLE
   C	 - COEFFICIENT VECTOR OF GIVEN EXPANSION
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
	   DOUBLE PRECISION VECTOR
   N	 - DIMENSION OF COEFFICIENT VECTOR C

REMARKS
   OPERATION IS BYPASSED IN CASE N LESS THAN 1

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   DEFINITION
   Y=SUM(C(I)*P(I-1,X), SUMMED OVER I FROM 1 TO N).
   EVALUATION IS DONE BY MEANS OF UPWARD RECURSION
   USING THE RECURRENCE EQUATION FOR LEGENDRE POLYNOMIALS
   P(N+1,X)=2*X*P(N,X)-P(N-1,X)-(X*P(N,X)-P(N-1,X))/(N+1).