Permutable functions concerning differential equations
2007 ◽
Vol 83
(3)
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pp. 369-384
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Keyword(s):
AbstractLet f and g be two permutable transcendental entire functions. Assume that f is a solution of a linear differential equation with polynomial coefficients. We prove that, under some restrictions on the coefficients and the growth of f and g, there exist two non-constant rational functions R1 and R2 such that R1 (f) = R(g). As a corollary, we show that f and g have the same Julia set: J(f) = J(g). As an application, we study a function f which is a combination of exponential functions with polynomial coefficients. This research addresses an open question due to Baker.
2013 ◽
Vol 21
(2)
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pp. 35-52
1958 ◽
Vol 22
(4)
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pp. 774-776
1992 ◽
Vol 38
(3)
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pp. 553-573
1871 ◽
Vol 19
(123-129)
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pp. 526-528
1870 ◽
Vol 18
(114-122)
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pp. 210-212
1988 ◽
Vol 40
(2)
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pp. 215-219
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2020 ◽
Vol DMTCS Proceedings, 28th...
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1975 ◽
Vol 78
(1)
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pp. 39-41
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Keyword(s):