Zeros of certain rational approximations to the cosecant (Q910883)

The authors study the zeros of the `truncations' \(f_ n(z)\) of the Mittag-Leffler expansion \[ f_{\infty}(z)=\pi \cos ec \pi z=\sum^{\infty}_{-\infty}(-1)^ m(z-m)^{-1}, \] giving precise bounds for their location: Each open half strip in the upper half plane whose base is the real interval \((-n+2h,-n+2h-2)\) contains exactly one zero of \(f_ n(z)\); the imaginary part of these zeros is asymptotically \(\pm (2/\pi)\log n\).