A Proof that extends hurwitz formula into the critical strip

AbstractHurwitz formula for the generalized zeta function ζ(s,a) has been established under condition Re(s = σ < 0. Using the same contour integral, the proof proposed in this paper allows the extension of this formula into the critical strip, 0 < σ < 1. A similar result is obtained for the related function (1Γ(s)) ∫0∞x−s–1(e−x)) dx, 0 < a ≤ 1