Published online by Cambridge University Press: 24 October 2008
Let {Sn} be the sequence of partial sums of the infinite seriesΣαn. Let {pn} be a sequence of constants real or complex and let us set
The sequence {tn} of Nörlund means (5) or simply (N, pn) means of the sequence {Sn} generated by the sequence of coefficients {pn} is defined by the following sequence -to-sequence transformation
The series ∑αn or the sequence {Sn} is said to be summable (N, pn) to the sum S, if
and is said to be absolutely summable (N, pn) or summable |N, pn|, if the sequence {tn} is of bounded variation, that is, the series ∑|tn − tn−1| is convergent (2).