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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
These concepts can be generalized in the case of hyperharmonic numbers.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri:There exist inversion relations between the original numbers and the corresponding numbers.
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Sonuç & Katkı:These concepts can be generalized in the case of hyperharmonic numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap
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