A method for deriving hypergeometric and related identities from the H² Hardy norm of conformal maps

2012/05/11 by Greg Markowsky, Markowsky, Greg · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1205.2458

arxiv created 2012/05/11 · openalex publication_date 2012/05/11 · arxiv updated 2012/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore a method which is implicit in a paper of Burkholder of identifying the H² Hardy norm of a conformal map with the explicit solution of Dirichlet's problem in the complex plane. Using the series form of the Hardy norm, we obtain an identity for the sum of a series obtained from the conformal map. We use this technique to evaluate several hypergeometric sums, as well as several sums that can be expressed as convolutions of the terms in a hypergeometric series.

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