fresnel
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constexpr std::pair<Complex, Complex> fresnel(const Complex &z) noexcept
Evaluates the Fresnel integrals [1] for a complex input.
Parameters
- const Complex &z
A complex number.
Returns
The Fresnel integrals are defined as:
\[\begin{split}S(z) = \int_{0}^{z}\sin(t^2)dt \\
C(z) = \int_{0}^{z}\sin(t^2)dt\end{split}\]
Example
Complex z = 1.0 + 1_j;
auto [S, C] = fresnel(z);
std::cout << S << "\n" << C << "\n";
Output:
-2.06189 + 2.06189j
2.55579 + 2.55579j
References