A NEW EXTENSION OF THE HURWITZ- LERCH ZETA FUNCTION AND PROPERTIES USING THE EXTENDED BETA FUNCTION \(B_{p,q}^{(ρ,σ,τ)}(x,y)\)

Abstract

The purpose of present paper is to introduce a new extension of Hurwitz-Lerch Zeta function by using the extended Beta function. Some recurrence relations, generating relations and integral representations are derived for that new extension.

Keywords

• extended beta function, extended hurwitz-lerch zeta function, recurrence relation, generating relation, integral representation.