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On the Convergence of a certain Multiple Series

Published online by Cambridge University Press:  24 October 2008

W. N. Bailey
W. N. Bailey
Affiliation:
Trinity College
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Extract

The theorem given by Professor Mordell in the preceding paper is capable of a slight generalisation. I first prove that the series

where 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, …

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 4 , October 1929 , pp. 410 - 411
Copyright
Copyright © Cambridge Philosophical Society 1929

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