Doklady Mathematics

, Volume 95, Issue 3, pp 240–242 | Cite as

A summation formula for divergent continued fractions

Mathematics

Abstract

Paradoxical formulas which have been proposed by a number of authors for evaluating divergent continued fractions are discussed. The point of the paradoxes is that limit passages (which are to be rigorously defined) result in the convergence real sequences to complex values. These formulas are refined and substantiated on the basis of the theory of uniform distribution supplemented with certain statements of complex analysis.

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References

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    G. H. Hardy, Divergent Series, 2nd ed. (Oxford Univ. Press, Oxford, 1949).MATHGoogle Scholar
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    S. Lang, Introduction to Diophantine Approximations (Addison-Wesley, Reading, Mass., 1966MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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