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.