• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.31-35
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• 2022

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

• 한국수학교육학회지시리즈A:수학교육
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• 제29권1호
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• pp.55-61
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• 1990

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.

• East Asian mathematical journal
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• 제17권1호
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• pp.147-158
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• 2001

The Gauss summation theorem plays a key role in the theory of(generalized) hypergeometric series. The authors study several proofs of the theorem and consider some applications of it.