2018/09/08 by Abdalla M. Aboarab, Aboarab, Abdalla M.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1809.02856
openalex publication_date 2018/09/08 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
An efficient procedure for the computation of Lis(z) where s<0 is here\npresented. We started with Polylogarithm Lis(z) where s<0. The summation\nof nszn is evaluated using a new method. An assumption is made that the\npower n is multiplied by x where x=1; then the series is integrated s\ntime in order to cancel the term ns out leaving the term zn. By simply\ntaking the derivative of the result s-times, an expression to evaluate the\nseries arises which include only a constant term and the sth order of\nderivative of the summation of a simple geometric series. The computation of\nLis(z) can then be performed in \O(n) operations.\n