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SUBROUTINE DTHEP

PURPOSE
   A SERIES EXPANSION IN HERMITE POLYNOMIALS WITH INDEPENDENT
   VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH INDEPENDENT
   VARIABLE Z, WHERE X=A*Z+B

USAGE
   CALL DTHEP(A,B,POL,N,C,WORK)

DESCRIPTION OF PARAMETERS
   A	 - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATION
	   DOUBLE PRECISION VARIABLE
   B	 - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION
	   DOUBLE PRECISION VARIABLE
   POL	 - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE)
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
	   DOUBLE PRECISION VECTOR
   N	 - DIMENSION OF COEFFICIENT VECTOR POL AND C
   C	 - COEFFICIENT VECTOR OF GIVEN EXPANSION
	   COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
	   POL AND C MAY BE IDENTICALLY LOCATED
	   DOUBLE PRECISION VECTOR
   WORK  - WORKING STORAGE OF DIMENSION 2*N
	   DOUBLE PRECISION ARRAY

REMARKS
   COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING
   WITH COEFFICIENT VECTOR POL.
   OPERATION IS BYPASSED IN CASE N LESS THAN 1.
   THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMS
   THE RANGE (-C,C) IN X TO THE RANGE (ZL,ZR) IN Z WHERE
   ZL=-(C+B)/A AND ZR=(C-B)/A.
   FOR GIVEN ZL, ZR AND C WE HAVE A=2C/(ZR-ZL) AND
   B=-C(ZR+ZL)/(ZR-ZL)

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   NONE

METHOD
   THE TRANSFORMATION 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.
   THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF
   X=A*Z+B TOGETHER WITH
   SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N)
   =SUM(C(I)*H(I-1,X), SUMMED OVER I FROM 1 TO N).