PDP-10 Archive: decus/20-0026/heps.doc from decus_20tap2

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SUBROUTINE HEPS

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

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

DESCRIPTION OF PARAMETERS
   Y	 - RESULT VALUE
   X	 - ARGUMENT VALUE
   C	 - COEFFICIENT VECTOR OF GIVEN EXPANSION
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
   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)*H(I-1,X), SUMMED OVER I FROM 1 TO N).
   EVALUATION IS DONE BY MEANS OF UPWARD RECURSION
   USING THE RECURRENCE EQUATION FOR HERMITE POLYNOMIALS
   H(N+1,X)=2*(X*H(N,X)-N*H(N-1,X)).