// Workers AI · traducción al español
Polilogaritmos incompletos
En matemáticas, la función polilogarítmica incompleta está relacionada con la función polilogarítmica. A veces se conoce como la integral incompleta de Fermi-Dirac o la integral incompleta de Bose-Einstein.
Traducción generada por IA. El artículo original en inglés continúa abajo.
// Workers AI · dad joke mode What did the incomplete polylogarithm say? I'm missing a log.
From Wikipedia, the free encyclopedia
In mathematics , the incomplete polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by:
Li
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{\displaystyle \operatorname {Li} _{s}(b,z)={\frac {1}{\Gamma (s)}}\int _{b}^{\infty }{\frac {x^{s-1}}{e^{x}/z-1}}~dx.}
Expanding about z=0 and integrating gives a series representation:
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{\displaystyle \operatorname {Li} _{s}(b,z)=\sum _{k=1}^{\infty }{\frac {z^{k}}{k^{s}}}~{\frac {\Gamma (s,kb)}{\Gamma (s)}}}
where Γ (s) is the gamma function and Γ (s,x) is the upper incomplete gamma function . Since Γ (s,0)=Γ (s), it follows that:
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{\displaystyle \operatorname {Li} _{s}(0,z)=\operatorname {Li} _{s}(z)}
where Lis (.) is the polylogarithm function.
