A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function

Cvijović, Đurđe

doi:10.1016/j.jmaa.2020.123972

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2020

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Cvijović, Đurđe

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Abstract

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-

Funding / projects:

Dynamics of nonlinear physicochemical and biochemical systems with modeling and predicting of their behavior under nonequilibrium conditions (RS-172015)

DOI: 10.1016/j.jmaa.2020.123972

ISSN: 0022-247X

WoS: 000522798600016

Scopus: 2-s2.0-85079892367

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https://vinar.vin.bg.ac.rs/handle/123456789/8832

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Vinča

TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8832
AB  - 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&gt;0 and s&gt;1 is strictly log-convex in s on (1,∞), whereas asζ⁎(s,a) for a,s&gt;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.
T2  - Journal of Mathematical Analysis and Applications
T1  - A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function
VL  - 487
IS  - 1
SP  - 123972
DO  - 10.1016/j.jmaa.2020.123972
ER  -

@article{
author = "Cvijović, Đurđe",
year = "2020",
abstract = "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&gt;0 and s&gt;1 is strictly log-convex in s on (1,∞), whereas asζ⁎(s,a) for a,s&gt;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.",
journal = "Journal of Mathematical Analysis and Applications",
title = "A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function",
volume = "487",
number = "1",
pages = "123972",
doi = "10.1016/j.jmaa.2020.123972"
}

Cvijović, Đ.. (2020). A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function. in Journal of Mathematical Analysis and Applications, 487(1), 123972.
https://doi.org/10.1016/j.jmaa.2020.123972

Cvijović Đ. A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function. in Journal of Mathematical Analysis and Applications. 2020;487(1):123972.
doi:10.1016/j.jmaa.2020.123972 .

Cvijović, Đurđe, "A note on convexity properties of functions related to the Hurwitz zeta and alternating Hurwitz zeta function" in Journal of Mathematical Analysis and Applications, 487, no. 1 (2020):123972,
https://doi.org/10.1016/j.jmaa.2020.123972 . .