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