Zeros of certain rational approximations to the cosecant
type: Item
instance of: scholarly article
title: Zeros of certain rational approximations to the cosecant
zbMATH Open document ID: 0697.30010
DOI: 10.1016/0022-247X(89)90031-0
author: Karl Dilcher
author: Kenneth B. Stolarsky
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: 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 \(\pm (2/\pi)\log n\).
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 4142385
zbMATH Keywords: Mittag-Leffler expansion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4142385