Preprint Article Version 1 This version is not peer-reviewed

On Multi-Order Logarithmic Polynomials and their Explicit Formulas, Recurrence Relations, and Inequalities

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.

Journal reference: Indagationes Mathematicae 2018, 29, 1179-1192
DOI: 10.1016/j.indag.2018.04.002

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.

Subject Areas

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

Comments (3)

Comment 1
Received: 30 April 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author of this paper
Comment: This preprint has been formally published by

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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Comment 2
Received: 13 September 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author of this preprint.
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Comment 3
Received: 14 September 2018
Commenter: Feng Qi
The commenter has declared there is no conflict of interests.
Comment: Feng Qi, On multivariate logarithmic polynomials and their properties, Indagationes Mathematicae 29 (2018), no. 5, 1179--1192; Available online at https://doi.org/10.1016/j.indag.2018.04.002
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