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Entire Solutions Of The Functional Equation f(f(z)) = g(z)

Published online by Cambridge University Press:  20 November 2018

W. J. Thron
W. J. Thron*
Affiliation:
University of Colorado
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In this note it is proved that: the functional equation

(1) f(f(z)) = g(z),

where g{z) is an entire function of finite order, which is not a polynomial, and which takes on a certain value p only a finite number of times, does not have a solution f(z) which is an entire function.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 47 - 48
Copyright
Copyright © Canadian Mathematical Society 1956

References

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