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This paper investigates an extended form of a beta function B p, q (x, y). We first study the convergence problem of the function B p, q (x, y) and consider the completely monotonic and log-convex properties of this function. As a result, we obtain a pair of Laguerre type inequalities. Next, we provide a new double integral representation for the function B p, q (x, y). Subsequently, we consider the convergence problem of the extended Hurwitz–Lerch zeta function Φ λ, μ; ν (z, s, a; p, q) defined by its series representation. Upon using the series manipulation techniques, we obtain two series identities. We also find various integral representations for the function Φ λ, μ; ν (z, s, a; p, q). Lastly, we apply Fourier analysis to the function z a Φ μ; ν (z, s, a; p, q) and obtain a Lindelöf–Wirtinger type expansion. Some interesting and promising results are also illustrated.