The Hurwitz zeta function: monotonicity, convexity and inequalities
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| 024 | 7 | 0 | |a 10.1007/s00010-015-0371-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-015-0371-1 | ||
| 100 | 1 | |a Alzer |D Horst |u Morsbacher Str. 10, 51545, Waldbröl, Germany |4 aut | |
| 245 | 1 | 4 | |a The Hurwitz zeta function: monotonicity, convexity and inequalities |h [Elektronische Daten] |c [Horst Alzer] |
| 520 | 3 | |a We present monotonicity and convexity properties of functions defined in terms of the Hurwitz zeta function $$\zeta(s, a)=\sum_{k=0}^\infty \frac{1}{(k+a)^s} \quad{(s > 1; \, a > 0)}$$ ζ ( s , a ) = ∑ k = 0 ∞ 1 ( k + a ) s ( s > 1 ; a > 0 ) and apply these results to obtain new inequalities involving $${\zeta(s, a)}$$ ζ ( s , a ) . Among others, we prove that the double-inequality $$\frac{1}{2} < a^s \zeta(s, a)+b^s \zeta(s, b)-(a+b)^s \zeta(s, a+b) < 1$$ 1 2 < a s ζ ( s , a ) + b s ζ ( s , b ) - ( a + b ) s ζ ( s , a + b ) < 1 holds for all s>1 and a, b > 0. Both bounds are sharp. | |
| 540 | |a Springer Basel, 2015 | ||
| 690 | 7 | |a Hurwitz zeta function |2 nationallicence | |
| 690 | 7 | |a monotonicity |2 nationallicence | |
| 690 | 7 | |a convexity |2 nationallicence | |
| 690 | 7 | |a inequalities |2 nationallicence | |
| 690 | 7 | |a Euler numbers |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer International Publishing |g 89/6(2015-12-01), 1401-1414 |x 0001-9054 |q 89:6<1401 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-015-0371-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-015-0371-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Alzer |D Horst |u Morsbacher Str. 10, 51545, Waldbröl, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer International Publishing |g 89/6(2015-12-01), 1401-1414 |x 0001-9054 |q 89:6<1401 |1 2015 |2 89 |o 10 | ||