Published online by Cambridge University Press: 09 April 2009
Let be a given series with its partial sums {Sn} and {Pn} a sequence of real or complex parameters. Write
. The transformation given by
defines the Nörlund means of {Sn} generated by {Pn}. The series Σann is said to be absolutely summable (N, pn) or summable ∣N, pn∣, if {tn} is of bounded variation, i.e., Σ|tn—tn−1| converges.