Affiliation:
1. Kahramanmaraş Sütçü İmam Üniversitesi
Abstract
In the paper, the authors discuss some extended results involving the Catalan numbers and establish an integral representation of the Catalan numbers in terms of the $(\alpha,k)$-gamma and $(\alpha,k)$-beta function. We refer to the results available in the literature by giving special values to the parameters in the obtained theorems.
Publisher
Turkish Journal of Mathematics and Computer Science, Association of Mathematicians
Reference12 articles.
1. Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279(2015), 57–66.
2. Andrews, G.E., Askey, R., Roy, R., Encyclopedia of Mathematics and its Applications. Special Functions, 1999.
3. Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer Science and Business Media, 1974.
4. Dana-Picard, T., Parametric integrals and Catalan numbers, International Journal of Mathematical Education in Science and Technology, 36(4)(2005), 410–414.
5. Iyiola, O.S., Nwaeze, E.R., Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl, 2(2)(2016), 115–122.