On Some Special Classes of Sonnenschein Matrices

Abstract

‎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 <br /> ‎[{a_{n,k}} = sumlimits_{v = 0}^k {left( begin{array}{l}‎<br /> ‎n‎<br /> ‎v‎<br /> ‎end{array} right){{left( {1‎ - ‎alpha‎ - ‎beta } right)}^v}{alpha ^{n‎ - ‎v}}left( begin{array}{l}‎<br /> ‎n‎ + ‎k‎ - ‎v‎ - ‎1‎<br /> ‎,,,,,,,,,,k‎ - ‎v‎<br /> ‎end{array} right)‎<br /> ‎{beta ^{k‎ - ‎v}}},] and calculate their row and column sums and give some applications of these sums‎.