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 polylogarithm [2016/05/30 16:40]nikolaj polylogarithm [2016/05/30 16:41] (current)nikolaj Both sides previous revision Previous revision 2016/05/30 16:41 nikolaj 2016/05/30 16:40 nikolaj 2016/05/30 16:40 nikolaj 2016/05/30 16:39 nikolaj 2016/05/30 16:38 nikolaj 2015/02/06 21:34 nikolaj 2015/02/06 21:21 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 20:44 nikolaj 2015/02/06 20:44 nikolaj 2015/02/06 20:43 nikolaj 2014/12/29 18:58 nikolaj 2014/12/29 18:58 nikolaj 2014/12/29 18:58 nikolaj old revision restored (2014/12/29 17:44) 2016/05/30 16:41 nikolaj 2016/05/30 16:40 nikolaj 2016/05/30 16:40 nikolaj 2016/05/30 16:39 nikolaj 2016/05/30 16:38 nikolaj 2015/02/06 21:34 nikolaj 2015/02/06 21:21 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 21:20 nikolaj 2015/02/06 20:44 nikolaj 2015/02/06 20:44 nikolaj 2015/02/06 20:43 nikolaj 2014/12/29 18:58 nikolaj 2014/12/29 18:58 nikolaj 2014/12/29 18:58 nikolaj old revision restored (2014/12/29 17:44) Line 1: Line 1: ===== Polylogarithm ===== ===== Polylogarithm ===== ==== Function ==== ==== Function ==== - | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Li}_s: ​?? \to ??$ | + >​Context:​ s + + | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Li}_s: ​{\mathbb C} \to {\mathbb C}$ | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Li}_s(z) := \begin{cases} \sum_{n=0}^\infty\,​ n^{-s} z^n&​\hspace{.5cm} \mathrm{if}\hspace{.5cm} |z|<​1,​\hspace{.5cm} \\\\ \text{analytic continuation}\hspace{.5cm} &​\hspace{.5cm} \mathrm{else} \end{cases}$ | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{Li}_s(z) := \begin{cases} \sum_{n=0}^\infty\,​ n^{-s} z^n&​\hspace{.5cm} \mathrm{if}\hspace{.5cm} |z|<​1,​\hspace{.5cm} \\\\ \text{analytic continuation}\hspace{.5cm} &​\hspace{.5cm} \mathrm{else} \end{cases}$ |