polykde (version 1.1.7)

polylog_minus_exp_mu: Polylogarithm function with negative argument

Description

Computation of the polylogarithm \(\mathrm{Li}_s(-e^\mu)\).

Usage

polylog_minus_exp_mu(mu, s, upper = Inf, ...)

Value

A vector of size length(mu) or length(s) with the values of the polylogarithm.

Arguments

mu

vector with exponents of the negative argument.

s

vector with indexes of the polylogarithm.

upper

upper limit of integration. Defaults to Inf.

...

further arguments passed to integrate, such as upper, abs.tol, rel.tol, etc.

Details

If s is an integer, 1/2, 3/2, or 5/2, then routines from the GSL library to compute Fermi--Dirac integrals are called. Otherwise, numerical integration is used.

Examples

polylog_minus_exp_mu(mu = 1:5, s = 1)
polylog_minus_exp_mu(mu = 1, s = 1:5)
polylog_minus_exp_mu(mu = 1:5, s = 1:5)