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- has the Fermi-Dirac Integral been solved?

hi guys

I have a question about whether or not the Fermi-Dirac Integral has Been solved, because i found a formula on Wikipedia that relates the Fermi-Dirac integral with the polylogarithm function:

$$F_{j}(x) = -Li_{j+1}(-e^{x})$$

and in some recent papers they claim that no analytical solution exist, plus if the formula on Wikipedia is correct why there are some recent papers discussing a Numerical solution for particular cases of the Fermi-Dirac integral?

I have a question about whether or not the Fermi-Dirac Integral has Been solved, because i found a formula on Wikipedia that relates the Fermi-Dirac integral with the polylogarithm function:

$$F_{j}(x) = -Li_{j+1}(-e^{x})$$

and in some recent papers they claim that no analytical solution exist, plus if the formula on Wikipedia is correct why there are some recent papers discussing a Numerical solution for particular cases of the Fermi-Dirac integral?