On the functional equation $f^n(z)+g^n(z)=e^{\alpha z+\beta}$

Qi Han; Feng Lü

doi:10.3103/s1068362319020067

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arXiv · 1612.06842

On the functional equation $f^n(z)+g^n(z)=e^{\alpha z+\beta}$

Qi Han·Feng Lü

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Abstract

We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{\alpha z+\beta}$ and $f^n(z)+f^n(z+c)=e^{\alpha z+\beta}$ ($c\neq0$) over the complex plane $\mathbf{C}$ for integers $n\geq1$.

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BibTeX RIS

Qi Han, Feng Lü. 2016-12-20. On the functional equation $f^n(z)+g^n(z)=e^{\alpha z+\beta}$. https://doi.org/10.3103/s1068362319020067

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