naginterfaces.library.sum.chebyshev(x, xmin, xmax, c, s)[source]

chebyshev evaluates a polynomial from its Chebyshev series representation at a set of points.

For full information please refer to the NAG Library document for c06dc

xfloat, array-like, shape

, the set of arguments of the series.


The lower end point of the interval .


The upper end point of the interval .

cfloat, array-like, shape

must contain the coefficient of the Chebyshev series, for .


Determines the series (see Notes).

The series is general.

The series is even.

The series is odd.

resfloat, ndarray, shape

The Chebyshev series evaluated at the set of points .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: , or .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, element , and .

Constraint: , for all .


chebyshev evaluates, at each point in a given set , the sum of a Chebyshev series of one of three forms according to the value of the parameter :




where lies in the range . Here is the Chebyshev polynomial of order in , defined by where .

It is assumed that the independent variable in the interval was obtained from your original variable , a set of real numbers in the interval , by the linear transformation

The method used is based upon a three-term recurrence relation; for details see Clenshaw (1962).

The coefficients are normally generated by other functions, for example they may be those returned by the interpolation function interp.dim1_cheb (in vector ), by a least squares fitting function in submodule fit, or as the solution of a boundary value problem by ode.bvp_coll_nth, ode.bvp_coll_sys or ode.bvp_ps_lin_solve.


Clenshaw, C W, 1962, Chebyshev Series for Mathematical Functions, Mathematical tables, HMSO