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ERIC Number: EJ799215
Record Type: Journal
Publication Date: 2008-Jul
Pages: 13
Abstractor: As Provided
Reference Count: 14
ISSN: ISSN-0020-739X
Analyticity without Differentiability
Kirillova, Evgenia; Spindler, Karlheinz
International Journal of Mathematical Education in Science and Technology, v39 n5 p587-599 Jul 2008
In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting properties of formal power series. Along the way, we show how formal power series can be used to solve combinatorial problems and also derive some results in calculus with a minimum of analytical machinery. (Contains 2 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A