New Expansion Formulas for a Family of the λ-Generalized Hurwitz-Lerch Zeta Functions - H. M. Srivastava; Sébastien Gaboury (International Journal of Mathematics and Mathematical Sciences)
We derive several new expansion formulas for a new family of the λ-generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014). 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.