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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hypertranscendence of the functional equation $ g(x\sp 2)=[g(x)]\sp 2+cx$


Author: Peter Borwein
Journal: Proc. Amer. Math. Soc. 107 (1989), 215-221
MSC: Primary 39B10; Secondary 30D05
MathSciNet review: 979226
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Abstract: The functional equation $ g({x^2}) = {[g(x)]^2} + cx$ has a unique nontrivial solution that is analytic at zero. We show, for $ c > 0$, that the solution of this equation satisfies no algebraic differential equation.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0979226-X
PII: S 0002-9939(1989)0979226-X
Article copyright: © Copyright 1989 American Mathematical Society