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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 Sayı: 6

Some applications on $q$-analog of the generalized hyperharmonic numbers of order $r,$ $ H_{n}^{r}(\alpha )$

Sibel KOPARAL
Neşe ÖMÜR
Cemile Duygu ÇOLAK
Pages
2094–2103
Publication Date
2020-12-08
DOI
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AI Summary & Key Takeaways

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

Finally, we examine new applications of an $n\times n$ matrix $A_{n}=\left[ a_{i,j}\right] $ with the terms $a_{i,j}=H_{i}^{r}(j,q).$

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define $q$-analog of the generalized harmonic numbers $H_{n}(\alpha )$ and the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}(\alpha ),$ and obtain some sums involving these numbers.
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Key Findings & Data:In this paper, we define $q$-analog of the generalized harmonic numbers $H_{n}(\alpha )$ and the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}(\alpha ),$ and obtain some sums involving these numbers.
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Conclusion & Impact:Finally, we examine new applications of an $n\times n$ matrix $A_{n}=\left[ a_{i,j}\right] $ with the terms $a_{i,j}=H_{i}^{r}(j,q).$
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized harmonic number · hyperharmonic number · q-analog

Abstract

In this paper, we define $q$-analog of the generalized harmonic numbers $H_{n}(\alpha )$ and the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}(\alpha ),$ and obtain some sums involving these numbers. Finally, we examine new applications of an $n\times n$ matrix $A_{n}=\left[ a_{i,j}\right] $ with the terms $a_{i,j}=H_{i}^{r}(j,q).$

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Cite This Article

KOPARAL, S., ÖMÜR, N., ÇOLAK, C. D. (2020). Some applications on $q$-analog of the generalized hyperharmonic numbers of order $r,$ $ H_{n}^{r}(\alpha )$. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 Sayı: 6, 2094–2103. https://ajindex.com/articles/929245

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