A Tauberian theorem for Borel summability
Published online by Cambridge University Press: 24 October 2008
Extract
1. We use Eα to denote the Euler transformation obtained as the special case of the Hausdorff transformation (H, μn) in which μn = αn (see [5], §§64, 72; in the notation of Hardy's book [1], our Eα is (E, q) with q = (1 − α)/α). Eα is regular if and only if 0 < α < 1, and in this range Eα increases in strength as α decreases since EαEβ = Eαβ. Also, E1 = I, the identity transformation.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 135 - 138
- Copyright
- Copyright © Cambridge Philosophical Society 1987
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