Published online by Cambridge University Press: 18 May 2009
Given a series we define
, by the relations
The series is said to be summable (C, k), where k > - 1, to the sum s if
to be summable (C, - 1) to s if it converges to s and nan = o(l); to be absolutely summable (C, k), or summable | C, k, to s if it is summable (C, k) to s and
and to be strongly Cesàro summable to s with order k > 0 and index p or summable [C; k, p] to s, if