Indian Journal of Pure and Applied Mathematics

, Volume 41, Issue 1, pp 39–66

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


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


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 seriesfactorial seriescontinued fractionshypergeometric continued fractionsSturmian sequences

Copyright information

© The Indian National Science Academy 2010

Authors and Affiliations

  1. 1.University of TrondheimTrondheimNorway
  2. 2.University of CaliforniaLos AngelesUSA