Summability of a Cauchy product series

Abstract

=0 > The Euler matrix is generated by the function g(z) = 1-r+rz, [4]. It is the purpose of this note to establish theorems of Abel's, Mertens' and Cauchy's type for the transpose of a regular Sonnenschein matrix generated by the function f(z). 2. Let the series, En?= oanXn, have radius of convergence equal to 1. The following notation is adopted from [3]. Let an*= E2% djnaj. If En o a* = A, then we write