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Trailing-Edge - PDP-10 Archives - decuslib20-02 - 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.