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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).
```