On the functional equation $f^n(z)+g^n(z)=e^{α z+β}$
Abstract
We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{α z+β}$ and $f^n(z)+f^n(z+c)=e^{α z+β}$ ($c\neq0$) over the complex plane $𝐂$ for integers $n≥1$.
We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{α z+β}$ and $f^n(z)+f^n(z+c)=e^{α z+β}$ ($c\neq0$) over the complex plane $𝐂$ for integers $n≥1$.