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On Multi-Order Logarithmic Polynomials and their Explicit Formulas, Recurrence Relations, and Inequalities
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Version 1
: Received: 9 September 2017 / Approved: 11 September 2017 / Online: 11 September 2017 (04:22:18 CEST)
A peer-reviewed article of this Preprint also exists.
Qi, F. On multivariate logarithmic polynomials and their properties. Indagationes Mathematicae 2018, 29, 1179-1192. Qi, F. On multivariate logarithmic polynomials and their properties. Indagationes Mathematicae 2018, 29, 1179-1192.
Abstract
In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the fi rst and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.
Keywords
multi-order logarithmic number; multi-order logarithmic polynomial; explicit formula; identity; recurrence relation; inversion theorem; Bell polynomial of the second kind; Stirling number; determinantal inequality; product inequality; completely monotonic function; logarithmic convexity; Faa di Bruno formula
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter's Conflict of Interests: I am the author of this paper
Feng Qi, On multivariate logarithmic polynomials and their properties, Indagationes Mathematicae 29 (2018), in press; Available online at https://doi.org/10.1016/j.indag.2018.04.002
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Commenter's Conflict of Interests: I am the author of this preprint.
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The commenter has declared there is no conflict of interests.