TY  - JOUR
T1  - Some applications on $q$-analog of the generalized hyperharmonic numbers of order $r,$ $ H_{n}^{r}(\alpha )$
AU  - Ömür, Neşe
AU  - Koparal, Sibel
AU  - Çolak, Cemile Duygu
PY  - 2020
DA  - December
DO  - 10.15672/hujms.580684
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 2094
EP  - 2103
VL  - 49
IS  - 6
LA  - en
AB  - 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 $a_{i,j}=H_{i}^{r}(j,q).$
KW  - Generalized harmonic number
KW  - hyperharmonic number
KW  - q-analog
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UR  - https://doi.org/10.15672/hujms.580684
L1  - https://dergipark.org.tr/en/download/article-file/1188032
ER  -