ekore 0.15.3

EKO expressions
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

//! Harmonic sums of weight 1.
use num::complex::Complex;

use crate::harmonics::cache::{Cache, K};
use crate::harmonics::polygamma::cern_polygamma;

/// Compute the harmonic sum $S_1(N)$.
///
/// $$S_1(N) = \sum\limits_{j=1}^N \frac 1 j = \psi_0(N+1)+\gamma_E$$
/// with $\psi_0(N)$ the digamma function and $\gamma_E$ the Euler-Mascheroni constant.
pub fn S1(N: Complex<f64>) -> Complex<f64> {
    cern_polygamma(N + 1.0, 0) + 0.577_215_664_901_532_9
}

/// Analytic continuation of harmonic sum $S_{-1}(N)$ for even moments.
pub fn Sm1e(c: &mut Cache) -> Complex<f64> {
    let hS1 = c.get(K::S1);
    let hS1h = c.get(K::S1h);
    hS1h - hS1
}

/// Analytic continuation of harmonic sum $S_{-1}(N)$ for odd moments.
pub fn Sm1o(c: &mut Cache) -> Complex<f64> {
    let hS1 = c.get(K::S1);
    let hS1mh = c.get(K::S1mh);
    hS1mh - hS1
}