New integral representations of the polylogarithm function

@article{Cvijovic2006NewIR,
  title={New integral representations of the polylogarithm function},
  author={Djurdje Cvijovic},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2006},
  volume={463},
  pages={897 - 905}
}
  • D. Cvijovic
  • Published 8 April 2007
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function Lis(z). The polylogarithm function appears in several fields of mathematics and in many physical problems. We, by making use of elementary arguments, deduce several new integral representations of the polylogarithm Lis(z) for any complex z for which |z|<1. Two are valid for… 
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  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2003
This paper summarizes the basic properties of the Euler dilogarithm function, often referred to as the Spence function. These include integral representations, series expansions, linear and quadratic
Integral representations of the Riemann Zeta function for odd-integer arguments
Handbook of Mathematical Functions with Formulas