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

Authors : Sibel KOPARAL, Neşe ÖMÜR, Cemile Duygu ÇOLAK

Pages : 2094-2103

Doi:10.15672/hujms.580684

View : 14 | Download : 4

Publication Date : 2020-12-08

Article Type : Research Paper

Abstract :In this paper, we define $q$-analog of the generalized harmonic numbers $H_{n}insert ignore into journalissuearticles values(\alpha );$ and the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}insert ignore into journalissuearticles values(\alpha );,$ 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 $a_{i,j}=H_{i}^{r}insert ignore into journalissuearticles values(j,q);.$
Keywords : Generalized harmonic number, hyperharmonic number, q analog