polylog
=======

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The polylog package provides Rust implementations of real and complex
polylogarithms, including the dilogarithm and trilogarithm.

The polylog package depends on the `num` crate.


Example
-------

```rust
use num::complex::Complex;
use polylog::{Li, Li0, Li1, Li2, Li3, Li4, Li5, Li6};

let x = 1.0;
let z = Complex::new(1.0, 1.0);
let n = 10;

// real polylogarithms for real arguments
println!("Li0({}) = {}", x, x.li0());      // Re[Li_0(x)]
println!("Li1({}) = {}", x, x.li1());      // Re[Li_1(x)]
println!("Li2({}) = {}", x, x.li2());      // Re[Li_2(x)] (dilogarithm)
println!("Li3({}) = {}", x, x.li3());      // Re[Li_3(x)] (trilogarithm)
println!("Li4({}) = {}", x, x.li4());      // Re[Li_4(x)]
println!("Li_{}({}) = {}", n, x, x.li(n)); // Re[Li_n(x)]

// complex polylogarithms for complex arguments
println!("Li0({}) = {}", z, z.li0());      // Li_0(z)
println!("Li1({}) = {}", z, z.li1());      // Li_1(z)
println!("Li2({}) = {}", z, z.li2());      // Li_2(z) (dilogarithm)
println!("Li3({}) = {}", z, z.li3());      // Li_3(z) (trilogarithm)
println!("Li4({}) = {}", z, z.li4());      // Li_4(z)
println!("Li5({}) = {}", z, z.li5());      // Li_5(z)
println!("Li6({}) = {}", z, z.li6());      // Li_6(z)
println!("Li_{}({}) = {}", n, z, z.li(n)); // Li_n(z)
```


Notes
-----

The implementation of the real dilogarithm is an adaptation of
[[arXiv:2201.01678](https://arxiv.org/abs/2201.01678)].

The implementation of the complex dilogarithm has been inspired by the
implementation in [SPheno](https://spheno.hepforge.org) and has been
translated to Rust.

The implementation of the real trilogarithm is an adaptation of
[[arXiv:2308.11619](https://arxiv.org/abs/2308.11619)].

The implementation of the general n-th order polylogarithm is an
adaptation of [[arXiv:2010.09860](https://arxiv.org/abs/2010.09860)].


Copying
-------

polylog is licenced under the GNU Lesser General Public License (GNU
LGPL) version 3.