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Year 2023, Volume: 15 Issue: 1, 164 - 170, 30.06.2023

Abdullah Akkurt Huseyin Yıldırım

https://doi.org/10.47000/tjmcs.1182387

Abstract

References

  • Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279(2015), 57–66.
  • Andrews, G.E., Askey, R., Roy, R., Encyclopedia of Mathematics and its Applications. Special Functions, 1999.
  • Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer Science and Business Media, 1974.
  • Dana-Picard, T., Parametric integrals and Catalan numbers, International Journal of Mathematical Education in Science and Technology, 36(4)(2005), 410–414.
  • 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.
  • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264(2014), 65–70.
  • Koshy, T., Catalan Numbers with Applications, Oxford University Press, 2008.
  • Lebedev, N.N., Silverman, R.A., Livhtenberg, D.B., Special functions and their applications, Physics Today, 18(12)(1965), 70.
  • Qi, F., Parametric integrals, the Catalan numbers, and the beta function, Elemente der Mathematik, 72(3)(2017), 103–110.
  • Qi, F., Akkurt, A., Yildirim, H., Catalan numbers, k-gamma and k-beta functions, and parametric integrals, J. Comput. Anal. Appl, 25(6)(2018), 1036–1042.
  • Sarıkaya, M.Z., Akkurt, A., Budak, H., T¨urkay, M. E.,Yildirim, H., On some special functions for conformable fractional integrals, Konuralp Journal of Mathematics , 8(2)(2020), 376–383 .
  • Shi, X.T., Liu, F. F., Qi, F., An integral representation of the Catalan numbers, Glob. J. Math. Anal, 3(3)(2015), 130–133.

Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function

Year 2023, Volume: 15 Issue: 1, 164 - 170, 30.06.2023

Abdullah Akkurt Huseyin Yıldırım

https://doi.org/10.47000/tjmcs.1182387

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.

Keywords

Catalan number $(\alpha,k)$-gamma function $(\alpha,k)$-beta function

References

  • Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279(2015), 57–66.
  • Andrews, G.E., Askey, R., Roy, R., Encyclopedia of Mathematics and its Applications. Special Functions, 1999.
  • Comtet, L., Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer Science and Business Media, 1974.
  • Dana-Picard, T., Parametric integrals and Catalan numbers, International Journal of Mathematical Education in Science and Technology, 36(4)(2005), 410–414.
  • 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.
  • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264(2014), 65–70.
  • Koshy, T., Catalan Numbers with Applications, Oxford University Press, 2008.
  • Lebedev, N.N., Silverman, R.A., Livhtenberg, D.B., Special functions and their applications, Physics Today, 18(12)(1965), 70.
  • Qi, F., Parametric integrals, the Catalan numbers, and the beta function, Elemente der Mathematik, 72(3)(2017), 103–110.
  • Qi, F., Akkurt, A., Yildirim, H., Catalan numbers, k-gamma and k-beta functions, and parametric integrals, J. Comput. Anal. Appl, 25(6)(2018), 1036–1042.
  • Sarıkaya, M.Z., Akkurt, A., Budak, H., T¨urkay, M. E.,Yildirim, H., On some special functions for conformable fractional integrals, Konuralp Journal of Mathematics , 8(2)(2020), 376–383 .
  • Shi, X.T., Liu, F. F., Qi, F., An integral representation of the Catalan numbers, Glob. J. Math. Anal, 3(3)(2015), 130–133.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Abdullah Akkurt 0000-0001-5644-1276

Huseyin Yıldırım 0000-0001-8855-9260

Publication Date June 30, 2023
Published in Issue Year 2023 Volume: 15 Issue: 1

Cite

APA Akkurt, A., & Yıldırım, H. (2023). Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function. Turkish Journal of Mathematics and Computer Science, 15(1), 164-170. https://doi.org/10.47000/tjmcs.1182387
AMA Akkurt A, Yıldırım H. Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function. TJMCS. June 2023;15(1):164-170. doi:10.47000/tjmcs.1182387
Chicago Akkurt, Abdullah, and Huseyin Yıldırım. “Catalan Numbers in Terms of $(\alpha, K)-$Gamma Function and $(\alpha, K)-$Beta Function”. Turkish Journal of Mathematics and Computer Science 15, no. 1 (June 2023): 164-70. https://doi.org/10.47000/tjmcs.1182387.
EndNote Akkurt A, Yıldırım H (June 1, 2023) Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function. Turkish Journal of Mathematics and Computer Science 15 1 164–170.
IEEE A. Akkurt and H. Yıldırım, “Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function”, TJMCS, vol. 15, no. 1, pp. 164–170, 2023, doi: 10.47000/tjmcs.1182387.
ISNAD Akkurt, Abdullah - Yıldırım, Huseyin. “Catalan Numbers in Terms of $(\alpha, K)-$Gamma Function and $(\alpha, K)-$Beta Function”. Turkish Journal of Mathematics and Computer Science 15/1 (June 2023), 164-170. https://doi.org/10.47000/tjmcs.1182387.
JAMA Akkurt A, Yıldırım H. Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function. TJMCS. 2023;15:164–170.
MLA Akkurt, Abdullah and Huseyin Yıldırım. “Catalan Numbers in Terms of $(\alpha, K)-$Gamma Function and $(\alpha, K)-$Beta Function”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 1, 2023, pp. 164-70, doi:10.47000/tjmcs.1182387.
Vancouver Akkurt A, Yıldırım H. Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function. TJMCS. 2023;15(1):164-70.