zeta
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constexpr double zeta(const double x) noexcept
Evaluates the Riemann zeta function [1] for a real input. Approximated via an integral representation [2].
Parameters
- const double z
A real number.
Returns
- double
A real number.
The Riemann zeta function is an infinite series defined as:
\[\zeta(n) = \sum_{n = 1}^{\infty} x^{-n}\]
It may also be expressed as the following integral:
\[\zeta(z) = \frac{1}{\Gamma(z)}\int_{0}^{\infty} \frac{t^{z - 1}}{e^t - 1} dt\]
for \(\Re(z) > 1\).
Example
double z = 2.0;
std::cout << zeta(z) << "\n";
Output:
1.64494
References