Linear independence of iterates of entire functions

Bernal González, Luis

doi:10.1090/S0002-9939-1991-1045136-4

Linear independence of iterates of entire functions
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by Luis Bernal González

Proc. Amer. Math. Soc. 112 (1991), 1033-1036

DOI: https://doi.org/10.1090/S0002-9939-1991-1045136-4

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Abstract:

We prove the following result: The set $\left \{ {{h_n}:n = 0,1, \ldots } \right \}$ is a linearly independent sequence of entire functions, where ${h_0} = 1,{h_1} = {g_{1,}}{h_2} = {g_1} \circ {g_2},{h_3} = {g_1} \circ {g_2} \circ {g_3}, \ldots ,{g_1}$ is a nonconstant entire function and ${g_n}(n \geq 2)$ are entire functions which are not polynomials of degree $\leq 1$. Our theorem generalizes a previous one about linear independence of iterates.

References

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On an integral function of an integral function

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