The dilogarithm function for complex argument

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Maximon Leonard C 2003The dilogarithm function for complex argumentProc. R. Soc. Lond. A.4592807–2819http://doi.org/10.1098/rspa.2003.1156SectionRestricted accessThe dilogarithm function for complex argument Leonard C Maximon Leonard C Maximon Department of Physics, The George Washington University, Washington, DC 20052, USA Google Scholar Find this author on PubMed Search for more papers by this author Leonard C Maximon Leonard C Maximon Department of Physics, The George Washington University, Washington, DC 20052, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2003https://doi.org/10.1098/rspa.2003.1156AbstractThis 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 transformations, functional relations, numerical values for special arguments and relations to the hypergeometric and generalized hypergeometric function. The basic properties of the two functions closely related to the dilogarithm (the inverse tangent integral and Clausen's integral) are also included. A brief summary of the defining equations and properties for the frequently used generalizations of the dilogarithm (polylogarithm, Nielsen's generalized polylogarithm, Jonquière's function, Lerch's function) is also given. A résumé of the earliest articles that consider the integral defining this function, from the late seventeenth century to the early nineteenth century, is presented. Critical references to details concerning these functions and their applications in physics and mathematics are listed. 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