Adams Basic Package > Adams View > View Command Language > panel > panel set twindow_function chebyshev_polynomial

panel set twindow_function chebyshev_polynomial

The CHEBYSHEV_POLYNOMIAL function evaluates a Chebyshev polynomial at a user specified value x. The SHIFT (that is, x0) and the COEFFICIENTS (that is, a0, a1,..., a30) parameters are used to define the constants for the Chebyshev polynomial. The Chebyshev polynomial is defined as:

C(x) =\ aj * Tj(x-x0)

where the functions Tj are recursively defined as:

Tj(x-x0) = 2 * (x-x0) * Tj-1(x-x0) - Tj-2(x-x0)

where

T0(x-x0) = 1, and

T1(x-x0) = x-x0.

The index "j" has a range from zero (0) to n, where n is the number of terms in the series.

Note that:

T2(x-x0) = 2 * (x- x0)**2 - 1

T3(x-x0) = 4 * (x- x0)**3 - 3 * (x- x0)

Format:

panel set twindow_function chebyshev_polynomial
x =	run time function
shift =	real
angular_shift =	angle
coefficients =	real
angular_coefficients =	angle

Description:

Parameter	Value Type	Description
x	Run Time Function	Specifies a run time function.
shift	Real	Specifies a real variable that is a non-angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function.
angular_shift	Angle	Specifies a real variable that is a non-angular shift in a Chebyshev polynomial, Fourier Cosine series, Fourier Sine series, or polynomial function. Or, a phase shift in the independent variable x, for a simple_harmonic_function.
coefficients,	Real	Specifies the non-angular real variables that define as many as thirty-one coefficients (a0, a1,..., a30) for the series or polynomial.
angular_coefficients	Angle	Specifies the angular real variables that define as many as thirty-one coefficients (a0, a1,..., a30) for the series or polynomial.