A simple proof of Tong's theorem
Vyacheslav M. Abramov
TL;DR
This paper offers a straightforward and clear proof of Tong's theorem, a variant of Kummer's test, utilizing a Hardy-Littlewood Tauberian theorem to simplify the understanding of the result.
Contribution
The paper introduces a new simple and transparent proof of Tong's theorem, enhancing clarity and accessibility compared to previous proofs.
Findings
Proof simplifies understanding of Tong's theorem
Utilizes Hardy-Littlewood Tauberian theorem for proof
Provides a more transparent approach to Kummer's test
Abstract
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
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Taxonomy
TopicsAutoimmune and Inflammatory Disorders · Metabolism and Genetic Disorders · Tumors and Oncological Cases