Asymptotics of diagonal Padé approximants of the functions $\sin z$, $\cos z$, $\operatorname{sinh}z$ and $\operatorname{cosh}z$

This paper studies properties of diagonal Padé approximants of the functions $\sin z$, $\cos z$, $\operatorname{sinh}z$ and $\operatorname{cosh}z$. It investigates asymptotic equations, at each $z\in\mathbf C$, for the difference between a given function and the corresponding diagonal Padé approximants.
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