Preprint Article Version 1 This version is not peer-reviewed

Integral Representations of Catalan Numbers and Their Applications

Version 1 : Received: 6 April 2017 / Approved: 7 April 2017 / Online: 7 April 2017 (04:27:13 CEST)

A peer-reviewed article of this Preprint also exists.

Journal reference: Mathematics 2017, 5, 40
DOI: 10.3390/math5030040

Abstract

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Subject Areas

Catalan number; integral representation; equivalent relation; application; sum of power series; Catalan--Qi function; Catalan--Qi number; beta function

Readers' Comments and Ratings (3)

Comment 1
Received: 13 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first author of this paper.
Comment: This preprint has been formally published as follows.

Feng Qi and Bai-Ni Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, 31 pages; Available online at http://dx.doi.org/10.3390/math5030040.
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Comment 2
Received: 5 January 2018
Commenter: Feng Qi (Click to see Publons profile: )
Commenter's Conflict of Interests: I am the first and corresponding author for this manuscript
Comment: Please cite this article as

Feng Qi and Bai-Ni Guo, Integral representations of the Catalan numbers and their applications, Mathematics 5 (2017), no. 3, Article 40, 31 pages; Available online at http://dx.doi.org/10.3390/math5030040
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Comment 3
Received: 24 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: There are typos in the second equation of Theorem 7.1 on page 23 in this preprint. These typos have been corrected by the second equation of Theorem 22 on page 22 in the paper at https://www.researchgate.net/publication/318674119_Integral_Representations_of_the_Catalan_Numbers_and_Their_Applications
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