Zero-free disks in families of analytic functions

  • J. Waldvoge
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1287)


This note is concerned with families of functions f(z,q), analytic in both the variable z∈ℂ and the parameter q∈ℂ. In the one-parameter subfamily characterized by q=e, ϑ∈ℝ we consider the problem of finding the zero z=zm of f(z,eiϑm) with minimum modulus. An algorithm for calculating ϑm, zm based on Newton’s method will be described. The problem arises in several fields of approximation theory, notably in connection with certain Padé approximants and with the Whittaker and the power series constants. Conjectured values of these constants will be given in extended precision.


Power Series Exponential Type Newton Step Michigan Math Closed Unit Disk 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. Waldvoge
    • 1
  1. 1.Applied Mathematics ETH-ZentrumZürichSwitzerland

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