New expansion formulas for a family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions (Q2330241)

Summary: We derive several new expansion formulas for a new family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions which were introduced by the first author [``A new family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functions with applications'', Appl. Math. Inf. Sci. 8, No. 4, 1485--1500 (2014), \url{http://www.naturalspublishing.com/Article.asp?ArtcID=5645}]. These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also considered.