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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

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

Sibel Koparal(Kocaeli University)0000-0001-9574-9652
Neşe Ömür(Kocaeli University)0000-0002-3972-9910
Cemile Duygu Çolak(Kocaeli University)0000-0002-2322-4395
Pages
—
Publication Date
2020-12-08
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AI Summary & Key Takeaways

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⚡ 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

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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, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.580684

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