Function spfunc::zeta::zeta

pub fn zeta<T: FromComplex>(s: T) -> T

Calculate the Riemann zeta function, which is defined as

$$\zeta(s)=\sum_{k=1}^{\infty}\frac{1}{k^{s}}$$

for $\mathfrak{R}[s]>1$.

And it has a unique analytic continuation to entire complex plane, excluding the point $s=1$.

Then, a globally convergent series for the Riemann zeta function is given by

$$\zeta(s)=\frac{1}{1-2^{1-s}}\sum_{n=0}^{\infty}\frac{1}{2^{n+1}}\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(k+1)^{1-s}$$