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Zeros of Hypergeometric Functions

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Abstract

For certain ranges of parameters, it is shown that the hypergeometric function F(a, b; b+1; z) has no zeros in a specified half-plane. It is also shown that the zeros of the hypergeometric polynomials

$$F(-n,\ kn\ + \ell\ + 1;\ kn\ + \ell\ + 2;\ z)$$

cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.

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Authors and Affiliations

  1. Department of Mathematics, Undergraduate Programs Office, University of Michigan, Ann Arbor, Michigan, 48109-1109, USA

    Kathryn Boggs

  2. Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109-1109, USA

    Peter Duren

Authors
  1. Kathryn Boggs
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  2. Peter Duren
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Correspondence to Kathryn Boggs.

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Boggs, K., Duren, P. Zeros of Hypergeometric Functions. Comput. Methods Funct. Theory 1, 275–287 (2001). https://doi.org/10.1007/BF03320990

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  • DOI: https://doi.org/10.1007/BF03320990

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