scipy.special.chebyc

scipy.special.chebyc(n, monic=False)

Chebyshev polynomial of the first kind on \([-2, 2]\).

Defined as \(C_n(x) = 2T_n(x/2)\), where \(T_n\) is the nth Chebychev polynomial of the first kind.

Parameters:

nint

Degree of the polynomial.

monicbool, optional

If True, scale the leading coefficient to be 1. Default is False.

Returns:

Corthopoly1d

Chebyshev polynomial of the first kind on \([-2, 2]\).

See also

chebyt

Chebyshev polynomial of the first kind.

Notes

The polynomials \(C_n(x)\) are orthogonal over \([-2, 2]\) with weight function \(1/\sqrt{1 - (x/2)^2}\).

References

[1]

Abramowitz and Stegun, “Handbook of Mathematical Functions” Section 22. National Bureau of Standards, 1972.