tn

constexpr Complex tn(int n, const Complex &z) noexcept: Evaluates the nth Chebyshev polynomial of the first kind [1] for a complex input.

Parameters

const Complex &z

A complex number.

const int n

A nonnegative integer.

Returns

type Complex

A complex number.

Chebyshev polynomials of the first kind can be defined as follows:

\[T_n(z) = \cos(n\cos^{-1}(z))\]

Example

Complex z = 1.0 + 1_j;
int n = 1;
std::cout << tn(n, z) << "\n";

Output:

1 + 1j

References