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- W2113138744 abstract "1. It is trivial that for all integers n ≥ 0 implies s n = 0 ( n = 0, 1, 2, …). This conclusion is no longer true if it is only known that (1·1) is true for an infinity of n. But we shall show that the truth of (1·1) for, roughly speaking, one-half of all positive integers, together with an order condition on the magnitude of s n , ensures s n = 0 for all n. This follows from Theorem 1. Let a 1 < a 2 < … be positive integers, n(R) the number of a's not exceeding R, s n a sequence of complex numbers. If (ii) s n = ο( n K ) as n tends to infinity then s n = P(n), where P(x) is a polynomial of degree less than K." @default.
- W2113138744 created "2016-06-24" @default.
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- W2113138744 date "1944-06-01" @default.
- W2113138744 modified "2023-10-18" @default.
- W2113138744 title "A theorem on finite differences with an application to the theory of Hausdorff summability" @default.
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- W2113138744 doi "https://doi.org/10.1017/s0305004100018302" @default.
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