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      Hardy's generalization of eᶻ and related analogs of cosine and sine

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      Author(s)
      Ostrovskii, I.
      Date
      2006
      Source Title
      Computational Methods and Function Theory
      Print ISSN
      1617-9447
      Electronic ISSN
      2195-3724
      Publisher
      Springer
      Volume
      6
      Issue
      1
      Pages
      1 - 14
      Language
      English
      Type
      Article
      Item Usage Stats
      85
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      26
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      Abstract
      In 1904, Hardy introduced an entire function depending on two parameters being a generalization of e z. He had studied in detail its asymptotic properties and that of its zeros. We consider the two following non-asymptotic problems related to the zeros. (i) Determine values of the parameters such that all the zeros belong to the open left half-plane. For these values, the analogs of sine and cosine generated by Hardy’s function have real, simple and interlacing zeros. (ii) Determine the number of real zeros as a function of the parameters.
      Keywords
      Class P
      Integral representation
      Levin's generalization of the Hermite - Biehler theorem
      Logarithmic derivative
      Rolle's theorem
      Permalink
      http://hdl.handle.net/11693/48572
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      • Department of Mathematics 653
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