Terminal Summation: Extending the Concept of Convergence

This paper presents an atypical method for summing divergent series, and provides a sum for the divergent series log(n). We use an idea of T.E. Phipps, called Terminal Summation, which uses asymptotic analysis to assign a value to divergent series. The method associates a series to an appropriate difference equations having boundary conditions at infinity, and solves the difference equations which then provide a value for the original series. We point out connections between Phipps\u27 method, the Euler-MacLaurin sum formula, the Ramanujan sum and other traditional methods for summing divergent series

On translativity of absolute Riesz summability

In this work we characterize translativity of the summability vertical bar R, p(n)vertical bar(k), k > 1, for any sequence (p(n)) without imposing the conditions given by Orhan [C. Orhan, Translativity of absolute weighted mean summability, Czechoslovak Math. J. 48 (1998) 755-761], and so deduce some known results. (C) 2010 Elsevier Ltd. All rights reserved