Araştırma Makalesi

Several properties of Racah polynomials

Cilt: 15 Sayı: 3 15 Eylül 2025
Mustafa Dumlupınar *
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Several properties of Racah polynomials

Abstract

In this paper, bilinear and bilateral generating functions for Racah polynomials are derived, along with a theorem that provides a systematic approach for obtaining these functions. Furthermore, a new recurrence relation and an integral representation for Racah polynomials are established, enhancing their analytical framework. Special attention is given to the limiting cases of Racah polynomials, including Hahn, dual Hahn and Meixner polynomials, for which new recurrence relations are obtained. In particular, a novel integral representation for the dual Hahn polynomial is introduced, offering additional insights into its structural properties. These results contribute to the broader understanding of orthogonal polynomials, enhancing their theoretical significance and potential applications. By expanding the known properties of these polynomials, the findings may provide a basis for further mathematical research and applications in areas such as combinatorics, mathematical physics, and special functions.

Keywords

Generating function , Hypergeometric function , Integral represantations , Racah polynomials , Recurrence relations

Kaynakça

  1. Agarwal, A. K., & Monocha, H. L. (1980). On some new generating functions. Matematicki Vesnik, 4(17)(32), 395–402.
  2. Aktaş, R., & Erkuş-Duman, E. (2015). A generalization of the extended Jacobi polynomials in two variables. Gazi University Journal of Science, 28(3), 503–521.
  3. Area, I., Godoy, E., Ronveaux, A., & Zarzo, A. (2004). Classical symmetric orthogonal polynomials of a discrete variable. Integral Transforms and Special Functions, 15(1), 1–12. https://doi.org/10.1080/10652460310001600672.
  4. Dumlupinar, M., & Erkus-Duman, E. (2023). Advances in the continuous dual Hahn polynomials. Journal of Mathematical Extension, 17(4), 1–18. https://doi.org/10.30495/JME.2023.2696.
  5. Erkus-Duman, E., & Choi, J. (2021). Gottlieb polynomials and their q-extensions. Mathematics, 9(13), 1499. https://doi.org/10.3390/math9131499.
  6. Geronimo, J. S., & Iliev, P. (2009). Bispectrality of multivariable Racah–Wilson polynomials. Constructive Approximation, 31, 417–457. https://doi.org/10.1007/s00365-009-9045-3.
  7. Gottlieb, M. J. (1938). Concerning some polynomials orthogonal on a finite or enumerable set of points. American Journal of Mathematics, 60(2), 453–458. https://doi.org/10.2307/2371307.
  8. Koekoek, R., Lesky, P. A., & Swarttouw, R. F. (2010). Hypergeometric Orthogonal Polynomials and Their q-Analogues. Springer.
  9. Korkmaz-Duzgun, D., & Erkus-Duman, E. (2018). The Laguerre type d-orthogonal polynomials. J. Sci. Arts, 42, 95-106.
  10. Ozmen, N., & Erkus-Duman, E. (2018). Some families of generating functions for the generalized Cesaro polynomials. Journal of Computational Analysis and Applications, 25, 1124–1127.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematiksel Yöntemler ve Özel Fonksiyonlar

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

15 Eylül 2025

Gönderilme Tarihi

17 Mart 2025

Kabul Tarihi

13 Ağustos 2025

Yayımlandığı Sayı

Yıl 2025 Cilt: 15 Sayı: 3

DOI

https://doi.org/10.17714/gumusfenbil.1660077

IZ

https://izlik.org/JA42EX49KT

Kaynak Göster

RIS / Bibtex
APA
Dumlupınar, M. (2025). Several properties of Racah polynomials. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 15(3), 809-818. https://doi.org/10.17714/gumusfenbil.1660077

e-ISSN: 2146-538X   Yayın Modeli: Sürekli Yayın   Atıf Dizinleri: TR Dizin , SCOPUS