Implements the complete Fermi-Dirac integral (Wikipedia)
The general implementaion uses Polylogarithms.jl, but there is also an approximaton for F(1/2,x) available.
The approximated version can be called like this:
julia> using FermiDiracIntegrals
julia> F(Val(1/2),1)
1.5676943564187247and the general polylogarithm implementation can be used like this:
julia> using FermiDiracIntegrals
julia> F(1/2,1)
1.575640776151315 - 0.0imBenchmark:
julia> using BenchmarkTools
julia> using FermiDiracIntegrals
julia> @btime F(1/2,1)
64.742 μs (18 allocations: 512 bytes)
1.575640776151315 - 0.0im
julia> @btime F(Val(1/2),1)
0.698 ns (0 allocations: 0 bytes)
1.5676943564187247