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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 5

On $q$-hypergeometric Bernoulli polynomials and numbers

Salifou Mboutngam(University of Maroua, Higher Teacher Training College)0000-0002-4560-0961
Patrick Njıonou Sadjang(University of Douala, Faculty of Industrial Engineering)0000-0002-5196-6855
Pages
—
Publication Date
2021-10-15
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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. (2021). On $q$-hypergeometric Bernoulli polynomials and numbers. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 5. https://doi.org/10.15672/hujms.669940

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