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- W4380135941 abstract "Let $S$ be a semigroup. We determine the complex-valued solutions $f,g,h$ of the functional equation begin{equation*}f(xy)=f(x)g(y)+g(x)f(y)+h(x)h(y), x,yin S,end{equation*} in terms of multiplicative functions, solutions of the special case $$varphi(xy)=varphi(x)chi(y)+chi(x)varphi(y), x,yin S$$ of the sine addition law, where $chi:Stomathbb{C}$ is a multiplicative function, and also in terms of solutions of the particular case $$psi(xy)=psi(x)chi(y)+chi(x)psi(y)+varphi(x)varphi(y), x,yin S$$ of the cosine-sine functional equation where $chi:Stomathbb{C}$ is a multiplicative function and $varphi:Stomathbb{C}$ such that the pair $(varphi,chi)$ satisfies the sine addition law." @default.
- W4380135941 created "2023-06-10" @default.
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- W4380135941 creator A5089989069 @default.
- W4380135941 date "2023-06-07" @default.
- W4380135941 modified "2023-09-24" @default.
- W4380135941 title "Cosine-sine functional equation on semigroups" @default.
- W4380135941 doi "https://doi.org/10.48550/arxiv.2306.04666" @default.
- W4380135941 hasPublicationYear "2023" @default.
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