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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 10 - Sayı: 1

On ($p, q$)-Rogers-Szegő Matrices

($p, q$)-Rogers-Szegő Matrisleri Üzerine

Adem ŞAHİN
Pages
285–294
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Keywords:($p, q$)-analogue; ($p, q$)-Rogers-Szegő polynomials; ($p, q$)-Rogers-Szegő matrix.

📌 3 Key Takeaways

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Objective & Hypothesis:In the present article, we have discussed the ($p, q$)-numbers, the Rogers-Szegő polynomial and the ($p, q$)-Rogers-Szegő polynomial and have defined the ($p, q$)-matrices and the ($p, q$)- Rogers-Szegő matrices.
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Key Findings & Data:We have presented some algebraic properties of these matrices and have proved them.
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Conclusion & Impact:Keywords:($p, q$)-analogue; ($p, q$)-Rogers-Szegő polynomials; ($p, q$)-Rogers-Szegő matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present article, we have discussed the ($p, q$)-numbers, the Rogers-Szegő polynomial and the ($p, q$)-Rogers-Szegő polynomial and have defined the ($p, q$)-matrices and the ($p, q$)- Rogers-Szegő matrices. We have presented some algebraic properties of these matrices and have proved them. In particular, we have obtained the factorization of these matrices, their inverse matrices, as well as the matrix representations of the ($p, q$)-numbers, the Rogers-Szegő polynomials and the ($p, q$)-Rogers-Szegő polynomials. Keywords:($p, q$)-analogue; ($p, q$)-Rogers-Szegő polynomials; ($p, q$)-Rogers-Szegő matrix.

Özet

Bu çalışmada, ($p, q$)-sayılarını, Rogers-Szegő polinomunu ve ($p, q$)-Rogers-Szegő polinomunu ele aldık ve ($p, q$)-matrislerini ve ($p, q$)-Rogers-Szegő matrislerini tanımladık. Bu matrislere ait bazı özellikleri verdik ve bunların ispatlarını yaptık. Özellikle, bu matrislerin çarpanlara ayrılışını, bunların ters matrislerini ve ($p, q$)-sayılarının, Rogers-Szegő polinomlarının ve ($p, q$)-Rogers-Szegő polinomlarının matris temsillerini elde ettik. Anahtar Kelimeler: ($p, q$)-analoji; ($p, q$)-Rogers-Szegő polinomu; ($p, q$)-Rogers-Szegő matrisi.

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Cite This Article

ŞAHİN, A. (2022). On ($p, q$)-Rogers-Szegő Matrices. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 - Sayı: 1, 285–294. https://ajindex.com/articles/428431

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