On Some Special Classes of Sonnenschein Matrices

Document Type: Research Paper


1 Vali-e-Asr University of Rafsanjan

2 Vali-e-Asr University



‎In this paper we consider the special classes of Sonnenschein matrices‎, ‎namely the Karamata matrices $K[\alpha,\beta]=\left(a_{n,k}\right)$ with the entries‎
‎\[{a_{n,k}} = \sum\limits_{v = 0}^k {\left( \begin{array}{l}‎
‎\end{array} \right){{\left( {1‎ - ‎\alpha‎ - ‎\beta } \right)}^v}{\alpha ^{n‎ - ‎v}}\left( \begin{array}{l}‎
‎n‎ + ‎k‎ - ‎v‎ - ‎1\\‎
‎\,\,\,\,\,\,\,\,\,\,k‎ - ‎v‎
‎\end{array} \right)‎
‎{\beta ^{k‎ - ‎v}}},\] and calculate their row and column sums and give some applications of these sums‎.


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