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Published online by Cambridge University Press: 20 January 2009
In a recent paper some general properties of γ-matrices were proved and Dienes' theorem on regular γ-matrices extended to semiregular γ-matrices and the binomial series. In section 2 of this paper the previous results will be extended to certain classes of Taylor series. Section 3 gives some new results on Borel's exponential summation, and section 4 introduces matrices efficient for Taylor series on the circle of convergence and others efficient for Dirichlet series on the line of convergence. A knowledge of the definitions and results of the paper mentioned above is assumed.
page 43 note 1 Vermes, P., “On γ-matrices and their application to the binomial series,” these Proceedings 8 (1947), 1–13. This paper will be referred to as γ-M.Google Scholar
page 43 note 2 Dienes, P., The Taylor Series (Oxford), 1931, 418. This book will be referred to as T.S.Google Scholar
page 43 note 3 γ-M, section 5.
page 44 note 1 Here G(i) denotes the i-th diminutixc of G, e.g. (3.1) of γ · M.
page 46 note 1 T.S. 401.
page 46 note 2 T.S. 401.
page 46 note 3 T.S. 419–420.
page 46 note 4 T.S. 403–404.
page 47 note 1 T.S. 305.
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