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Hypergeometric Functions and Carlitz Differential Equations over Function Fields

  • Anatoly N. Kochubei
Part of the Progress in Mathematics book series (PM, volume 260)

Abstract

The paper is a survey of recent results in analysis of additive functions over function fields motivated by applications to various classes of special functions including Thakur’s hypergeometric function. We consider basic notions and results of calculus, analytic theory of differential equations with Carlitz derivatives (including a counterpart of regular singularity), umbral calculus, holonomic modules over the Weyl-Carlitz ring.

Keywords

Function fields Thakur’s hypergeometric function differential equations with Carlitz derivative umbral calculus holonomic modules 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Anatoly N. Kochubei
    • 1
  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKievUkraine

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