Remark on a double-inequality for the Riemann zeta function |
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| Authors: | Horst Alzer |
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| Institution: | Morsbacher Str. 10, D-51545 Waldbröl, Germany |
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| Abstract: | Let ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have(1-δ(x))ζ(x)+αδ(x)<ζ(x+1)<(1-δ(x))ζ(x)+βδ(x), | with the best possible constant factorsThis improves a recently published result of Cerone et al., J. Inequalities Pure Appl. Math. 5(2) (43) (2004), who showed that the double-inequality holds with and .
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| Keywords: | Riemann zeta function Inequalities |
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