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chbevl
Evaluate Chebyshev series.SYNOPSIS:
int N;
double x, y, coef[N], chebevl();
y = chbevl(x, coef, N);
DESCRIPTION:
Evaluates the series
N-1
- '
y = > coef[i] T (x/2)
- i
i=0
of Chebyshev polynomials Ti at argument x/2.
Coefficients are stored in reverse order, i.e. the zero order term is last in the array. Note N is the number of coefficients, not the order. If coefficients are for the interval a to b, x must have been transformed to x -> 2(2x - b - a)/(b-a) before entering the routine. This maps x from (a, b) to (-1, 1), over which the Chebyshev polynomials are defined.
If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, 1/a), the transformation required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity, this becomes x -> 4a/x - 1.
SPEED:
Taking advantage of the recurrence properties of the Chebyshev polynomials, the routine requires one more addition per loop than evaluating a nested polynomial of the same degree.
JavaScript:
var y = cephes.chbevl(x, coef, N);