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Abel Summability of Gap Series
Keating, J.P.; Reade, J.B.
HPLBRIMS9803
Keyword(s): Poisson summation formula; gap series
Abstract: We show how the Poisson summation formula can be used to investigate the Abel summability of gap series. We use the method to prove that the series ?08 (1)nxn2 is Abel summable, but that the series ?08 (1)nx2n isn't. Hardy obtained essentially the same result as ours concerning the latter series in[1]. Our proof is shorter and more elementary. We give some numerical estimates for the size of the oscillation of the series ?08(1)nxn2 as x? 1_.
6 Pages
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