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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 5

On $q$-hypergeometric Bernoulli polynomials and numbers

Salifou Mboutngam
Patrick Njionou Sadjang
Pages
1251–1267
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Classical results are recovered by limit transition.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce $q$-analogues of the hypergeometric Bernoulli polynomials in one and two real parameters and study several of their properties.
📊
Key Findings & Data:Also we provide the inversion, the power representation, the multiplication and the addition formula for these polynomials.
💡
Conclusion & Impact:Classical results are recovered by limit transition.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$q$-Bernoulli polynomials · $q$-Bernoulli numbers · $q$-hypergeometric Bernoulli polynomials

Abstract

We introduce $q$-analogues of the hypergeometric Bernoulli polynomials in one and two real parameters and study several of their properties. Also we provide the inversion, the power representation, the multiplication and the addition formula for these polynomials. Classical results are recovered by limit transition.

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Cite This Article

Mboutngam, S., Sadjang, P. N. (2022). On $q$-hypergeometric Bernoulli polynomials and numbers. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 5, 1251–1267. https://ajindex.com/articles/529527

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