BIT Numerical Mathematics

, Volume 29, Issue 2, pp 356–360

The practical use of the Euler transformation

  • R. E. Scraton
Part II Numerical Mathematics

DOI: 10.1007/BF01952689

Cite this article as:
Scraton, R.E. BIT (1989) 29: 356. doi:10.1007/BF01952689


The generalised Euler transformation is a powerful transformation of infinite series which can be used, in theory, for the acceleration of convergence and for analytic continuation. When the transformation is applied to a series with rounded coefficients, its behaviour can differ substantially from that predicted theoretically. In general, analytic continuation is impossible in this case. It is still possible, however, to use the transformation for acceleration of convergence, but some changes are necessary in the method of choosing the optimum parameter value.

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© BIT Foundations 1989

Authors and Affiliations

  • R. E. Scraton
    • 1
  1. 1.Department of Mathematics and ComputingSultan Qaboos UniversityAl-Khod, MuscatSultanate of Oman