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Published in:
2007 | OriginalPaper | Chapter
Hypergeometric Functions and Carlitz Differential Equations over Function Fields
Author : Anatoly N. Kochubei
Published in: Arithmetic and Geometry Around Hypergeometric Functions
Publisher: Birkhäuser Basel
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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.