Conditions for the equivalence of power series and discrete power series methods of summability

Abstract

Discrete power series methods were introduced and  their regularity results were developed by Watson \cite{watson2}. It was shown by Watson that discrete power series method $(P_\lambda)$ strictly includes corresponding power series method $(P)$. In the present work we present theorems showing when $(P_\lambda)$ and $(P)$ are equivalent methods and when two discrete power series methods are equivalent.