On the Convergence of a certain Multiple Series

Abstract

The theorem given by Professor Mordell in the preceding paper is capable of a slight generalisation. I first prove that the serieswhere α, β, γ, … are positive, converges only when κ > Σ (a′/α), the summation referring to those exponents a′ of a, b, c, … for which a ≥ 0; or, if there are no such exponents, the series converges only when κ > a/α, k > b/β, …