  In this paper we study summability based on double sequences of complex
constants as it is defined in "Linear Operators, General Theory" by N. Dunford
and J. T. Schwartz. We define "power double sequences" or infinite "power
matrices" as certain generalizations of double sequences and power series. We
relate the summability and boundedness of the power double sequences to the
summability and boundedness of the double sequence \textit{A}. While others do
investigate "power matrices" their definitions, as far as we were able to find,
differ from our definitions. Using these definitions we extend some summability
results for double sequences of constants to our power double sequences. We
investigate also other possible generalizations of double sequences and assess
their usefulness in summability study.
