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decuslib20-02
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decus/20-0026/dlap.doc
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SUBROUTINE DLAP
PURPOSE
COMPUTE THE VALUES OF THE LAGUERRE POLYNOMIALS L(N,X)
FOR ARGUMENT VALUE X AND ORDERS 0 UP TO N.
USAGE
CALL DLAP(Y,X,N)
DESCRIPTION OF PARAMETERS
Y - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES
OF LAGUERRE POLYNOMIALS OF ORDER 0 UP TO N
FOR GIVEN ARGUMENT X.
DOUBLE PRECISION VECTOR.
VALUES ARE ORDERED FROM LOW TO HIGH ORDER
X - ARGUMENT OF LAGUERRE POLYNOMIAL
DOUBLE PRECISION VARIABLE.
N - ORDER OF LAGUERRE 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
LAGUERRE POLYNOMIALS L(N,X)
L(N+1,X)=2*L(N,X)-L(N-1,X)-((1+X)*L(N,X)-L(N-1,X))/(N+1),
WHERE THE FIRST TERM IN BRACKETS IS THE ORDER,
THE SECOND IS THE ARGUMENT.
STARTING VALUES ARE L(0,X)=1, L(1,X)=1.-X.