25.12 Polylogarithms25.14 Lerch’s Transcendent

§25.13 Periodic Zeta Function

The notation \mathop{F\/}\nolimits\!\left(x,s\right) is used for the polylogarithm \mathop{\mathrm{Li}_{{s}}\/}\nolimits\!\left(e^{{2\pi ix}}\right) with x real:

25.13.1 \mathop{F\/}\nolimits\!\left(x,s\right)=\sum _{{n=1}}^{\infty}\frac{e^{{2\pi inx}}}{n^{s}},

where \realpart{s}>1 if x is an integer, \realpart{s}>0 otherwise.