Research Article

Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials

Volume: 11 Number: 4 December 30, 2024
EN

Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials

Abstract

The aim of this article is to derive some novel formulas and finite sums covering Stirling type numbers, the Frobenius Euler numbers and polynomials, the beta-type rational functions, and combinatorial numbers with the help of both generating functions and their functional equations, and also some special identities associated with special numbers and polynomials.

Keywords

References

  1. Carlitz, L., & Sholander, M. (1963). The product of two Eulerian polynomials. Mathematics Magazine, 36(1), 37–41. https://doi.org/10.2307/2688134
  2. Gun, D., & Simsek, Y. (2020). Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers. Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matematicas, 114(4), 167. https://doi.org/10.1007/s13398-020-00899-z
  3. Gun, D., & Simsek, Y. (2023). Modification exponential Euler type splines derived from Apostol-Euler numbers and polynomials of complex order. Applicable Analysis and Discrete Mathematics, 17(1), 197–215. https://doi.org/10.2298/AADM220712011G
  4. Kucukoglu, I., & Simsek, Y. (2019). Identities and relations on the q-Apostol type Frobenius-Euler numbers and polynomials. Journal of the Korean Mathematical Society, 56(1), 265–284. https://doi.org/10.4134/JKMS.j180185
  5. Luo, Q.-M. (2006). Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwanese Journal of Mathematics, 10(4), 917–925. https://doi.org/10.11650/twjm/1500403883
  6. Simsek, Y. (2013a). Identities associated with generalized Stirling type numbers and Eulerian type polynomials. Mathematical and Computational Applications, 18(3), 251-263. https://doi.org/10.3390/mca18030251
  7. Simsek, Y. (2013b). Generating functions for generalized Stirling type numbers, array type polynomials, Eulerian type polynomials and their applications. Fixed Point Theory and Algorithms for Sciences and Engineering, 87. https://doi.org/10.1186/1687-1812-2013-87
  8. Simsek, Y. (2015). Beta-type polynomials and their generating functions. Applied Mathematics and Computation, 254, 172–182. https://doi.org/10.1016/j.amc.2014.12.118

Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Publication Date

December 30, 2024

Submission Date

November 13, 2024

Acceptance Date

December 14, 2024

Published in Issue

Year 2024 Volume: 11 Number: 4

APA
Gün, D., & Şimşek, Y. (2024). Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials. Gazi University Journal of Science Part A: Engineering and Innovation, 11(4), 792-800. https://doi.org/10.54287/gujsa.1584764
AMA
1.Gün D, Şimşek Y. Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials. GU J Sci, Part A. 2024;11(4):792-800. doi:10.54287/gujsa.1584764
Chicago
Gün, Damla, and Yılmaz Şimşek. 2024. “Formulas and Finite Sums Covering Beta-Type Rational Functions and Euler-Frobenius-Type Polynomials”. Gazi University Journal of Science Part A: Engineering and Innovation 11 (4): 792-800. https://doi.org/10.54287/gujsa.1584764.
EndNote
Gün D, Şimşek Y (December 1, 2024) Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials. Gazi University Journal of Science Part A: Engineering and Innovation 11 4 792–800.
IEEE
[1]D. Gün and Y. Şimşek, “Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials”, GU J Sci, Part A, vol. 11, no. 4, pp. 792–800, Dec. 2024, doi: 10.54287/gujsa.1584764.
ISNAD
Gün, Damla - Şimşek, Yılmaz. “Formulas and Finite Sums Covering Beta-Type Rational Functions and Euler-Frobenius-Type Polynomials”. Gazi University Journal of Science Part A: Engineering and Innovation 11/4 (December 1, 2024): 792-800. https://doi.org/10.54287/gujsa.1584764.
JAMA
1.Gün D, Şimşek Y. Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials. GU J Sci, Part A. 2024;11:792–800.
MLA
Gün, Damla, and Yılmaz Şimşek. “Formulas and Finite Sums Covering Beta-Type Rational Functions and Euler-Frobenius-Type Polynomials”. Gazi University Journal of Science Part A: Engineering and Innovation, vol. 11, no. 4, Dec. 2024, pp. 792-00, doi:10.54287/gujsa.1584764.
Vancouver
1.Damla Gün, Yılmaz Şimşek. Formulas and Finite Sums Covering Beta-type Rational Functions and Euler-Frobenius-type Polynomials. GU J Sci, Part A. 2024 Dec. 1;11(4):792-800. doi:10.54287/gujsa.1584764