Araştırma Makalesi
Yıl 2020,
Cilt: 49 Sayı: 6, 2094 - 2103, 08.12.2020
Öz
Kaynakça
- [1] G.E. Andrews, The Theory of Partitions, Addison-Wesley, Reading Mass., 1976.
- [2] M. Bahşi and S. Solak, An application of hyperharmonic numbers in matrices, Hacet. J. Math. Stat. 42 (4), 387–393, 2013.
- [3] A.T. Benjamin, D. Gaebler and R. Gaebler, A combinatorial approach to hyperharmonic numbers, Integers, 3, 1–9, 2003.
- [4] A.T. Benjamin, G.O. Preston and J.J. Quinn, A Stirling encounter with harmonic numbers, Math. Mag. 75 (2), 95–103, 2002.
- [5] J.H. Conway and R.K. Guy, The Book of Numbers, Copernicus, 1996.
- [6] M. Genčev, Binomial sums involving harmonic numbers, Math. Slovaca, 61 (2), 215– 226, 2011.
- [7] H.W. Gould, Combinatorial Identities, Morgantown, W. Va., 1972.
- [8] C. Kızılateş and N. Tuğlu, Some combinatorial identities of q-harmonic and qhyperharmonic numbers, Communications in Mathematics and Applications 6 (2), 33–40, 2015.
- [9] T. Mansour and M. Shattuck, A q-analog of the hyperharmonic numbers, Afrika Mat. 25 (1), 147–160, 2014.
- [10] N. Ömür and G. Bilgin, Some applications of the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}(\alpha )$, Adv. Appl. Math. Sci. 17 (9), 617–627, 2018.
- [11] N. Ömür and S. Koparal, On the matrices with the generalized hyperharmonic numbers of order r, Asian-Eur. J. Math. 11 (3), 1850045, 2018.
- [12] J.M. Santmyer, A Stirling like sequence of rational numbers, Discrete Math. 171 (1-3), 229–235, 1997.
- [13] M. Sved, Gaussians and binomials, Ars Combin. 17-A, 325–351, 1984.
Some applications on $q$-analog of the generalized hyperharmonic numbers of order $r,$ $ H_{n}^{r}(\alpha )$
Öz
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 $a_{i,j}=H_{i}^{r}(j,q).$
Anahtar Kelimeler
Kaynakça
- [1] G.E. Andrews, The Theory of Partitions, Addison-Wesley, Reading Mass., 1976.
- [2] M. Bahşi and S. Solak, An application of hyperharmonic numbers in matrices, Hacet. J. Math. Stat. 42 (4), 387–393, 2013.
- [3] A.T. Benjamin, D. Gaebler and R. Gaebler, A combinatorial approach to hyperharmonic numbers, Integers, 3, 1–9, 2003.
- [4] A.T. Benjamin, G.O. Preston and J.J. Quinn, A Stirling encounter with harmonic numbers, Math. Mag. 75 (2), 95–103, 2002.
- [5] J.H. Conway and R.K. Guy, The Book of Numbers, Copernicus, 1996.
- [6] M. Genčev, Binomial sums involving harmonic numbers, Math. Slovaca, 61 (2), 215– 226, 2011.
- [7] H.W. Gould, Combinatorial Identities, Morgantown, W. Va., 1972.
- [8] C. Kızılateş and N. Tuğlu, Some combinatorial identities of q-harmonic and qhyperharmonic numbers, Communications in Mathematics and Applications 6 (2), 33–40, 2015.
- [9] T. Mansour and M. Shattuck, A q-analog of the hyperharmonic numbers, Afrika Mat. 25 (1), 147–160, 2014.
- [10] N. Ömür and G. Bilgin, Some applications of the generalized hyperharmonic numbers of order $r,$ $H_{n}^{r}(\alpha )$, Adv. Appl. Math. Sci. 17 (9), 617–627, 2018.
- [11] N. Ömür and S. Koparal, On the matrices with the generalized hyperharmonic numbers of order r, Asian-Eur. J. Math. 11 (3), 1850045, 2018.
- [12] J.M. Santmyer, A Stirling like sequence of rational numbers, Discrete Math. 171 (1-3), 229–235, 1997.
- [13] M. Sved, Gaussians and binomials, Ars Combin. 17-A, 325–351, 1984.
Toplam 13 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 8 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 49 Sayı: 6 |