Some Properties of Analytic Functions Defined by Polylogarithm Functions

The evolution of polylogarithm function, also known as Jonquiere’s function, was started in 1696 bytwo eminent mathematicians, Leibniz and Bernoulli . In their work, the polylogarithm functionwas defined using an absolute convergent series. The development of this function was so significantthat it was utilized in the research work of other prominent mathematicians such as Euler, Spence,Abel, Lobachevsky, Rogers, Ramanujan, etc., allowing them to discover various functional identitiesof great importance as a result . It should come as no surprise that the increased utilizationof the polylogarithm function appears to be related to its importance in a number of key areas ofmathematics and physics such as topology, algebra, geometry, complex analysis quantum field theory,and mathematical physics The main purpose of this paper, is to introduce a new subclass of analytic functionsinvolving Polylogarithm functions and obtain coefficient inequalities, distortion properties, extremepoints, radii of starlikeness and convexity, Hadamard product, and convolution and integral operatorsfor the class..