Families of Integrals of Polylogarithmic Functions

Mathematics

Anthony Sofo¹ 

[1] Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia;

关键词: Euler sums;    zeta functions;    Dirichlet functions;    series representation;    harmonic number;   

DOI  :  10.3390/math7020143

来源: DOAJ

【 摘 要 】

We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and polylogarithmic functions. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given. Suggestions for further research are also suggested, including a study of polylogarithmic functions with inverse trigonometric functions.

【 授权许可】

Unknown