kummer, function, mathematics, there, several, functions, known, known, confluent, hypergeometric, function, kummer, another, defined, below, related, polylogarithm, both, named, ernst, kummer, defined, displaystyle, lambda, frac, duplication, formula, display. In mathematics there are several functions known as Kummer s function One is known as the confluent hypergeometric function of Kummer Another one defined below is related to the polylogarithm Both are named for Ernst Kummer Kummer s function is defined by L n z 0 z log n 1 t 1 t d t displaystyle Lambda n z int 0 z frac log n 1 t 1 t dt The duplication formula is L n z L n z 2 1 n L n z 2 displaystyle Lambda n z Lambda n z 2 1 n Lambda n z 2 Compare this to the duplication formula for the polylogarithm Li n z Li n z 2 1 n Li n z 2 displaystyle operatorname Li n z operatorname Li n z 2 1 n operatorname Li n z 2 An explicit link to the polylogarithm is given by Li n z Li n 1 k 1 n 1 k 1 log k z k Li n k z n 1 n 1 L n 1 L n z displaystyle operatorname Li n z operatorname Li n 1 sum k 1 n 1 k 1 frac log k z k operatorname Li n k z frac n 1 n 1 left Lambda n 1 Lambda n z right References EditLewin Leonard ed 1991 Structural Properties of Polylogarithms Providence RI American Mathematical Society ISBN 0 8218 4532 2 This mathematical analysis related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Kummer 27s function amp oldid 1048049307, wikipedia, wiki, book, books, library,