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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:

n : int

Degree of the polynomial.

monic : bool, optional

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

Returns:

C : orthopoly1d

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

[R390]

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