Indian Journal of Pure and Applied Mathematics

, Volume 41, Issue 1, pp 39-66

First online:

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

  • Trond DigernesAffiliated withUniversity of Trondheim Email author 
  • , V. S. VaradarajanAffiliated withUniversity of California

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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