%0 Journal Article %1 eberl2023polylogarithm %A Eberl, Manuel %D 2023 %J Archive of Formal Proofs %K graph_theory mathematics polylogarithm_function %T The Polylogarithm Function %U https://www.isa-afp.org/entries/Polylog.html %X This entry provides a definition of the Polylogarithm function, commonly denoted as . Here, is a complex number and an integer parameter. This function can be defined by the power series expression for and analytically extended to the entire complex plane, except for a branch cut on . Several basic properties are also proven, such as the relationship to the Eulerian polynomials via for , the derivative formula , the relation to the “normal” logarithm via , and the duplication formula .

@article{eberl2023polylogarithm, abstract = {This entry provides a definition of the Polylogarithm function, commonly denoted as . Here, is a complex number and an integer parameter. This function can be defined by the power series expression for and analytically extended to the entire complex plane, except for a branch cut on . Several basic properties are also proven, such as the relationship to the Eulerian polynomials via for , the derivative formula , the relation to the “normal” logarithm via , and the duplication formula .}, added-at = {2023-11-24T13:16:14.000+0100}, author = {Eberl, Manuel}, biburl = {https://www.bibsonomy.org/bibtex/2005436ca1f9a37b629bc348dfdafc358/tabularii}, description = {The Polylogarithm Function - Archive of Formal Proofs}, interhash = {5e9f668fd709971478053bf3bc679d5f}, intrahash = {005436ca1f9a37b629bc348dfdafc358}, issn = {2150-914x}, journal = {Archive of Formal Proofs}, keywords = {graph_theory mathematics polylogarithm_function}, month = {November}, note = {https://isa-afp.org/entries/Polylog.html, Formal proof development}, timestamp = {2023-11-24T17:01:56.000+0100}, title = {The Polylogarithm Function}, url = {https://www.isa-afp.org/entries/Polylog.html}, year = 2023 }