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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
These concepts can be generalized in the case of hyperharmonic numbers.
📌 3 Key Takeaways
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Objective & Hypothesis:It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices.
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Key Findings & Data:There exist inversion relations between the original numbers and the corresponding numbers.
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Conclusion & Impact:These concepts can be generalized in the case of hyperharmonic numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Harmonic numbers · hyperharmonic numbers · recurrence relations
Abstract
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
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Cite This Article
KOMATSU, T., PİZARRO-MADARİAGA, A. (2019). Harmonic numbers associated with inversion numbers in terms of determinants. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 340–354. https://ajindex.com/articles/215007