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43,50145/heps.doc
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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)).