TSP (libtsp/FN) - FNevChebP

## FNevChebP

#### Routine

double FNevChebP (double x, const float c[], int N)

#### Purpose

Evaluate a series expansion in Chebyshev polynomials

#### Description

The series expansion in Chebyshev polynomials is defined as

                N-1
         Y(x) = SUM c(i) T(i,x) ,
                i=0

where N is the number of terms in the expansion, c(i) is the coefficient for the i'th Chebyshev polynomial, and T(i,x) is the i'th order Chebyshev polynomial evaluated at x.

The Chebyshev polynomials satisfy the recursion

      T(i,x) = 2x T(i-1,x) - T(i-2,x),

with the initial conditions T(0,x)=1 and T(1,x)=x. This routine evaluates the expansion using a backward recursion.

#### Parameters

<- double FNevChebP
  Resultant value
-> double x
  Input value
-> const float c[]
  Array of coefficient values. c[i] is the coefficient of the i'th order Chebyshev polynomial.
-> int N
  Number of coefficients

#### Author / revision

P. Kabal Copyright (C) 1997 / Revision 1.11 1997/10/14

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