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On the Theory of Continued Fractions

Published online by Cambridge University Press:  20 January 2009

Haripada Datta
Haripada Datta
Affiliation:
Research Student, Edinburgh University.
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An analytic function is generally given either directly as a power-series, or at anyrate in some form which can readily be converted into a power-series. The power-series is not an altogether satisfactory method of representing the function, on account of the failure of its convergence outside its circle of convergence; in this respect it is decidedly inferior to the method of representing the function by a continued fraction, as this latter expression in many cases converges over the whole plane, except on certain curves.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , February 1915 , pp. 109 - 132
Copyright
Copyright © Edinburgh Mathematical Society 1916