Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 15 Sayı: 1, 164 - 170, 30.06.2023

Abdullah Akkurt Huseyin Yıldırım

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

Öz

Kaynakça

  • 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

Yıl 2023, Cilt: 15 Sayı: 1, 164 - 170, 30.06.2023

Abdullah Akkurt Huseyin Yıldırım

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Abdullah Akkurt 0000-0001-5644-1276

Huseyin Yıldırım 0000-0001-8855-9260

Yayımlanma Tarihi 30 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 15 Sayı: 1

Kaynak Göster

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. Haziran 2023;15(1):164-170. doi:10.47000/tjmcs.1182387
Chicago Akkurt, Abdullah, ve Huseyin Yıldırım. “Catalan Numbers in Terms of $(\alpha, K)-$Gamma Function and $(\alpha, K)-$Beta Function”. Turkish Journal of Mathematics and Computer Science 15, sy. 1 (Haziran 2023): 164-70. https://doi.org/10.47000/tjmcs.1182387.
EndNote Akkurt A, Yıldırım H (01 Haziran 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 ve H. Yıldırım, “Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function”, TJMCS, c. 15, sy. 1, ss. 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 (Haziran 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 ve Huseyin Yıldırım. “Catalan Numbers in Terms of $(\alpha, K)-$Gamma Function and $(\alpha, K)-$Beta Function”. Turkish Journal of Mathematics and Computer Science, c. 15, sy. 1, 2023, ss. 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.