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XII.—Solution of the Equation zez = a*

Published online by Cambridge University Press:  14 February 2012

E. M. Wright
E. M. Wright
Affiliation:
University of Aberdeen.
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Synopsis

The roots of the equation zez = a are of importance in several theories. Various authors have studied certain of their properties over more than a century. Here we solve the equation, in the sense that we define the sequence {Zn} of roots and, except for a small, finite number of values of n, find a rapidly convergent series for Zn. The terms in this series are alternately real and purely imaginary and so the series is very convenient for calculation. For the few remaining roots, we give practicable methods of numerical calculation and supply an auxiliary table.

The main results of this article have been announced without proof or details in Wright 1959.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 2 , 1959 , pp. 193 - 203
Copyright
Copyright © Royal Society of Edinburgh 1959

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