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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 5

On generalized Mathieu series and its companions

P. Cerone0000-0002-0271-431X
C. Lenard0000-0003-4819-0125
Pages
—
Publication Date
2019-10-08
DOI
—
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AI Summary & Key Takeaways

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

It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series.
📊
Key Findings & Data:The bounds are procured mainly using results pertaining to the Čebyšev functional.
💡
Conclusion & Impact:It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:companion generalized Mathieu series · identities and bounds · Čebyšev functional

Abstract

Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series. The bounds are procured mainly using results pertaining to the Čebyšev functional. The relationship to Zeta type functions are also examined. It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.

🔖

Cite This Article

Cerone, P., Lenard, C. (2019). On generalized Mathieu series and its companions. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 5. https://ajindex.com/articles/1402736

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