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decus_20tap2_198111
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decus/20-0026/dcnp.doc
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SUBROUTINE DCNP
PURPOSE
COMPUTE THE VALUES OF THE CHEBYSHEV POLYNOMIALS T(N,X)
FOR ARGUMENT VALUE X AND ORDERS 0 UP TO N.
USAGE
CALL DCNP,Y,X,N)
DESCRIPTION OF PARAMETERS
Y - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES
OF CHEBYSHEV POLYNOMIALS OF ORDER 0 UP TO N
FOR GIVEN ARGUMENT X.
DOUBLE PRECISION VECTOR.
VALUES ARE ORDERED FROM LOW TO HIGH ORDER
Y - RESULT VALUE
DOUBLE PRECISION VARIABLE.
X - ARGUMENT OF CHEBYSHEV POLYNOMIAL
N - ORDER OF CHEBYSHEV 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
CHEBYSHEV POLYNOMIALS T(N,X)
T(N+1,X)=2*X*T(N,X)-T(N-1,X),
WHERE THE FIRST TERM IN BRACKETS IS THE ORDER,
THE SECOND IS THE ARGUMENT.
STARTING VALUES ARE T(0,X)=1, T(1,X)=X.