In the present paper certain subclasses of strongly starlike and strongly convex functions defined by convolution with the generalized Hurwitz -Lerch Zeta function are investigated. Some inclusion relations are also mentioned as special cases of our main results.

A quadruple integral involving the logarithmic, exponential and polynomial functions is derived in terms of Lerch function. Special cases this are evaluated special fundamental constants. Almost all have an asymmetrical zero-distribution. The majority results work new.

Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification solving many significant problems astrophysics physics. In this present work, our aim is to demonstrate solutions the generalized Hurwitz-Lerch Zeta function by applying Sumudu transform. addition these, conditions generalised derived.

Series acceleration formulas are obtained for Dirichlet series with periodic coefficients. Special cases include Ramanujan’s formula for the values of the Riemann zeta function at the odd positive integers exceeding two, and related formulas for values of Dirichlet L-series and the Lerch zeta function.

Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through use extended generalized Noor-type integral operator associated with ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties this are also studied.

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...