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Trailing-Edge - PDP-10 Archives - decus_20tap2_198111 - 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.