<p>function polylogarithm 
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Li} _{-2}(z)=\sum _{k=1}^{\infty }{z^{k} \over k^{-2}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>Li</mi><mrow class="MJX-TeXAtom-ORD"><mo>−<!-- − --></mo><mn>2</mn></mrow></msub><mo>⁡<!-- ⁡ --></mo><mo stretchy="false">(</mo><mi>z</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>∑<!-- ∑ --></mo><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">∞<!-- ∞ --></mi></mrow></munderover><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>z</mi><mrow class="MJX-TeXAtom-ORD"><mi>k</mi></mrow></msup><msup><mi>k</mi><mrow class="MJX-TeXAtom-ORD"><mo>−<!-- − --></mo><mn>2</mn></mrow></msup></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \operatorname {Li} _{-2}(z)=\sum _{k=1}^{\infty }{z^{k} \over k^{-2}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5df8a1279f1f3129b85b8ca1eb8f6cd9124490a4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:18.551ex; height:6.843ex;" alt="{\displaystyle \operatorname {Li} _{-2}(z)=\sum _{k=1}^{\infty }{z^{k} \over k^{-2}}}"></span></dd></dl>
in the complex plane
<a href="//commons.wikimedia.org/wiki/User:Jan_Homann" title="User:Jan Homann">Jan Homann</a>
made with mathematica, own work