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decus/20-0026/hep.doc
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SUBROUTINE HEP
PURPOSE
COMPUTE THE VALUES OF THE HERMITE POLYNOMIALS H(N,X)
FOR ARGUMENT VALUE X AND ORDERS 0 UP TO N.
USAGE
CALL HEP(Y,X,N)
DESCRIPTION OF PARAMETERS
Y - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES
OF HERMITE POLYNOMIALS OF ORDER 0 UP TO N
FOR GIVEN ARGUMENT X.
VALUES ARE ORDERED FROM LOW TO HIGH ORDER
X - ARGUMENT OF HERMITE POLYNOMIAL
N - ORDER OF HERMITE 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
HERMITE POLYNOMIALS H(N,X)
H(N+1,X)=2*(X*H(N,X)-N*H(N-1,X))
WHERE THE FIRST TERM IN BRACKETS IS THE INDEX,
THE SECOND IS THE ARGUMENT.
STARTING VALUES ARE H(0,X)=1, H(1,X)=2*X.