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decuslib20-02
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decus/20-0026/csp.doc
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SUBROUTINE CSP
PURPOSE
COMPUTE THE VALUES OF THE SHIFTED CHEBYSHEV POLYNOMIALS
TS(N,X) FOR ARGUMENT X AND ORDERS 0 UP TO N.
USAGE
CALL CSP(Y,X,N)
DESCRIPTION OF PARAMETERS
Y - RESULT VECTOR OF DIMENSION N+1 CONTAINING THE VALUES
OF SHIFTED CHEBYSHEV POLYNOMIALS OF ORDER 0 UP TO N
FOR GIVEN ARGUMENT X.
VALUES ARE ORDERED FROM LOW TO HIGH ORDER
X - ARGUMENT OF SHIFTED CHEBYSHEV POLYNOMIAL
N - ORDER OF SHIFTED 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
SHIFTED CHEBYSHEV POLYNOMIALS TS(N,X)
TS(N+1,X)=(4*X-2)*TS(N,X)-TS(N-1,X),
WHERE THE FIRST TERM IN BRACKETS IS THE ORDER,
THE SECOND IS THE ARGUMENT.
STARTING VALUES ARE TS(0,X)=1, TS(1,X)=2*X-1.