Preprint Article Version 1 This version is not peer-reviewed

Some Properties of the Fuss–Catalan Numbers

Version 1 : Received: 13 August 2017 / Approved: 15 August 2017 / Online: 15 August 2017 (08:36:23 CEST)

A peer-reviewed article of this Preprint also exists.

Feng Qi and Pietro Cerone, \textit{Some properties of the Fuss--Catalan numbers}, Mathematics \textbf{6} (2018), no.~12, Article~277, 12~pages; Available online at \url{https://doi.org/10.3390/math6120277}. Feng Qi and Pietro Cerone, \textit{Some properties of the Fuss--Catalan numbers}, Mathematics \textbf{6} (2018), no.~12, Article~277, 12~pages; Available online at \url{https://doi.org/10.3390/math6120277}.

Journal reference: Mathematics 2018, 6, 277
DOI: 10.3390/math6120277

Abstract

In the paper, the authors express the FussCatalan numbers as several forms in terms of the CatalanQi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the FussCatalan numbers, and derive a double inequality for bounding the FussCatalan numbers.

Subject Areas

expression; analytic property; Fuss–Catalan number; Catalan–Qi function; Catalan number; monotonicity; logarithmic convexity; complete monotonicity; minimality; inequality

Comments (1)

Comment 1
Received: 24 November 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: Feng Qi and Pietro Cerone, Some properties of the Fuss–Catalan numbers, Mathematics 6 (2018), no. 12, Article 277, 12 pages; Available online at https://doi.org/10.3390/math6120277
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