한국수학교육학회지시리즈A:수학교육 (The Mathematical Education)
- 제29권1호
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- Pages.55-61
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- 1990
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- 1225-1380(pISSN)
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- 2287-9633(eISSN)
A Generalization of Abel's Theorem on Power Series
초록
There are three objectives of this paper. First, we present an elegant and simple generalization of Abel's theorem (i .e. tile Abel summability (on the unit disk of the euclidean plane) is regular). Second, we consider the definition of Abel summability through lim (equation omitted) which immediately has clear connexctions with CeSARO summability and Cesaro sums (equation omitted). This approach examplifies some simple aspects of so-called Tauberian theorems of divergent series. Third, we present the applications of the previous results to find the limits of transition probabilities of homogeneous Marker chain. Finally, we explain why the original Abel's theorem which looks obvious is difficult to be proved, and can not be proved analytically.
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