C C .................................................................. C C SUBROUTINE LAP C C PURPOSE C COMPUTE THE VALUES OF THE LAGUERRE POLYNOMIALS L(N,X) C FOR ARGUMENT VALUE X AND ORDERS 0 UP TO N. C C USAGE C CALL LAP(Y,X,N) C C DESCRIPTION OF PARAMETERS C Y - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES C OF LAGUERRE POLYNOMIALS OF ORDER 0 UP TO N C FOR GIVEN ARGUMENT X. C VALUES ARE ORDERED FROM LOW TO HIGH ORDER C X - ARGUMENT OF LAGUERRE POLYNOMIAL C N - ORDER OF LAGUERRE POLYNOMIAL C C REMARKS C N LESS THAN 0 IS TREATED AS IF N WERE 0 C C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED C NONE C C METHOD C EVALUATION IS BASED ON THE RECURRENCE EQUATION FOR C LAGUERRE POLYNOMIALS L(N,X) C L(N+1,X)=2*L(N,X)-L(N-1,X)-((1+X)*L(N,X)-L(N-1,X))/(N+1), C WHERE THE FIRST TERM IN BRACKETS IS THE ORDER, C THE SECOND IS THE ARGUMENT. C STARTING VALUES ARE L(0,X)=1, L(1,X)=1.-X. C C .................................................................. C SUBROUTINE LAP(Y,X,N) C DIMENSION Y(1) C C TEST OF ORDER Y(1)=1. IF(N)1,1,2 1 RETURN C 2 Y(2)=1.-X IF(N-1)1,1,3 C C INITIALIZATION 3 T=1.+X C DO 4 I=2,N 4 Y(I+1)=Y(I)-Y(I-1)+Y(I)-(T*Y(I)-Y(I-1))/FLOAT(I) RETURN END