Submitted:
09 September 2017
Posted:
11 September 2017
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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
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
