A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function
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© 2020 Elsevier Inc.
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Using the Hurwitz zeta and the alternating Hurwitz zeta function, ζ(s,a) and ζ⁎(s,a), it was shown through classical analysis and in a straightforward and unified manner that asζ(s,a) with a>0 and s>1 is strictly log-convex in s on (1,∞), whereas asζ⁎(s,a) for a,s>0 is strictly concave in s on (0,∞). As an immediate consequence, convexity properties of the Riemann zeta function as well as the Dirichlet beta, eta and lambda function were deduced. © 2020 Elsevier Inc.
Keywords:Convex function / Log-convex function / Dirichlet eta function / Riemann zeta function / Hurwitz zeta function; Alternating Hurwitz zeta function
Source:Journal of Mathematical Analysis and Applications, 2020, 487, 1, 123972-
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