Notes on Euler’swork on divergent factorial series and their associated continued fractions

Trond Digernes () and V. S. Varadarajan ()
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Trond Digernes: University of Trondheim
V. S. Varadarajan: University of California

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 39-66

Abstract: Abstract Factorial series which diverge everywhere were first considered by Euler from the point of view of summing divergent series. He discovered a way to sum such series and was led to certain integrals and continued fractions. His method of summation was essentialy what we call Borel summation now. In this paper, we discuss these aspects of Euler’s work from the modern perspective.

Keywords: Divergent series; factorial series; continued fractions; hypergeometric continued fractions; Sturmian sequences (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0019-8

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