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}.
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}.
Abstract
In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.
Computer Science and Mathematics, Computational Mathematics
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.
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
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author