Notes on Euler’swork on divergent factorial series and their associated continued fractions Authors Trond Digernes V. S. Varadarajan Article

First Online: 11 April 2010 DOI :
10.1007/s13226-010-0019-8

Cite this article as: Digernes, T. & Varadarajan, V.S. Indian J Pure Appl Math (2010) 41: 39. doi:10.1007/s13226-010-0019-8
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.

Key words
Divergent series
factorial series
continued fractions
hypergeometric continued fractions
Sturmian sequences

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