C C .................................................................. C C SUBROUTINE HEPS C C PURPOSE C COMPUTES THE VALUE OF AN N-TERM EXPANSION IN HERMITE C POLYNOMIALS WITH COEFFICIENT VECTOR C FOR ARGUMENT VALUE X. C C USAGE C CALL HEPS(Y,X,C,N) C C DESCRIPTION OF PARAMETERS C Y - RESULT VALUE C X - ARGUMENT VALUE C C - COEFFICIENT VECTOR OF GIVEN EXPANSION C COEFFICIENTS ARE ORDERED FROM LOW TO HIGH C N - DIMENSION OF COEFFICIENT VECTOR C C C REMARKS C OPERATION IS BYPASSED IN CASE N LESS THAN 1 C C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED C NONE C C METHOD C DEFINITION C Y=SUM(C(I)*H(I-1,X), SUMMED OVER I FROM 1 TO N). C EVALUATION IS DONE BY MEANS OF UPWARD RECURSION C USING THE RECURRENCE EQUATION FOR HERMITE POLYNOMIALS C H(N+1,X)=2*(X*H(N,X)-N*H(N-1,X)). C C .................................................................. C SUBROUTINE HEPS(Y,X,C,N) C DIMENSION C(1) C C TEST OF DIMENSION IF(N)1,1,2 1 RETURN C 2 Y=C(1) IF(N-2)1,3,3 C C INITIALIZATION 3 H0=1. H1=X+X C DO 4 I=2,N H2=X*H1-FLOAT(I-1)*H0 H0=H1 H1=H2+H2 4 Y=Y+C(I)*H0 RETURN END