Generalized Volterra functions, its integral representations and applications to the Mathieu-type series

Khaled Mehrez and Sergei M. Sitnik

Applied Mathematics and Computation, 2019, vol. 347, issue C, 578-589

Abstract: In this paper we introduce the new class of generalized Volterra functions. We prove some integral representations for them via Fox–Wright H-functions and Meijer G-functions. From positivity conditions on the weight in these representations, we found sufficient conditions on parameters of the generalized Volterra function to prove its complete monotonicity. As applications, a Turán type inequality for generalized Volterra functions is derived, infinite integral of some special functions are expressed in terms of the generalized Volterra functions and closed-form integral representations for a family of convergent Mathieu-type series defined in terms of generalized Volterra functions are established.

Keywords: Generalized Volterra functions; Complete monotonicity; Log-convex functions; Turán type inequalities; Mathieu-type series (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:578-589

DOI: 10.1016/j.amc.2018.11.004

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