The PolyLog.jl package provides Julia implementations of real and complex polylogarithms, including the real and complex dilogarithm and trilogarithm.

Example

using PolyLog
# real polylogarithms for real arguments
reli1(1.0)          # Re[Li_1(x)]
reli2(1.0)          # Re[Li_2(x)] (dilogarithm)
reli3(1.0)          # Re[Li_3(x)] (trilogarithm)
reli4(1.0)          # Re[Li_4(x)]
reli(10, 1.0)       # Re[Li_n(x)] for all integers n (here: n = 10)
# complex polylogarithms for real or complex arguments
li0(1.0 + 1.0im)    # Li_0(z)
li1(1.0 + 1.0im)    # Li_1(z)
li2(1.0 + 1.0im)    # Li_2(z) (dilogarithm)
li3(1.0 + 1.0im)    # Li_3(z) (trilogarithm)
li4(1.0 + 1.0im)    # Li_4(z)
li5(1.0 + 1.0im)    # Li_5(z)
li6(1.0 + 1.0im)    # Li_6(z)
li(10, 1.0 + 1.0im) # Li_n(z) for all integers n (here: n = 10)

Documentation

https://docs.juliahub.com/PolyLog/

Notes

The implementation of the real dilogarithm is an adaptation of [ arXiv:2201.01678 ].

The implementation of the complex dilogarithm has been inspired by the implementation in SPheno and has been translated to Julia.

The implementation of the general n-th order polylogarithm is an adaptation of [ arXiv:2010.09860 ].

Copying

PolyLog.jl is licenced under the MIT License.

Links

Refer to the package Polylogarithms.jl for a Julia implementation of polylogarithms of arbitrary complex order.