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Published online by Cambridge University Press: 20 January 2009
The theorems given here deal with the efficiency, mutual consistency, and regularity of γ-transformations.
§1. Theorem 1. The necessary and sufficient conditions that γ-matrices are efficient for all divergent series whose partial sums are bounded, are
where Δgk(a)≡gk(a)−gk+1(a).
page 123 note 1 All these terms and others used here are explained in Dienes, P., The Taylor Series (Oxford). 1931, Chapter 12. A knowledge of this chapter is assumed. The book will be referied to as D.Google Scholar
page 123 note 2 See p. 394 of D.
page 127 note 1 See VII, p. 399 of D after noting that G and G are row-finite.
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