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XXVI.—Solution of the Equation (z + b)eZ+a = ±(z − b)

Published online by Cambridge University Press:  14 February 2012

E. M. Wright
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Synopsis

The roots of these equations are of importance in several theories and various authors have studied certain of their properties. Here we solve the equations in the sense that we define two numbers z(1), z(0), and a sequence {zn} which include the roots of both equations. Except for a small, finite number of values of n, we find a rapidly convergent series for zn whose terms are alternately real and purely imaginary. We give a number of expansions and a variety of practical methods which enable us to calculate the small number of remaining roots to any required degree of accuracy.

The main results of this article have been announced without proof or details in Wright 1960.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 4 , 1961 , pp. 358 - 371
Copyright
Copyright © Royal Society of Edinburgh 1961

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References

REFERENCES TO LITERATURE

Wright, E. M., 1959 a. Bull. Amer. Math. Soc., 65, 89–93.CrossRefGoogle Scholar
Wright, E. M., 1959 b. Proc. Roy. Soc. Edin., A, 65, 193–203.Google Scholar
Wright, E. M., 1960. Bull. Amer. Math. Soc., 66, 277–281.CrossRefGoogle Scholar
Wright, E. M., 1961. J. Soc. Indust, Appl. Math., 9, 136–148.CrossRefGoogle Scholar