English

A method for deriving hypergeometric and related identities from the $H^2$ Hardy norm of conformal maps

Complex Variables 2012-05-14 v1

Abstract

We explore a method which is implicit in a paper of Burkholder of identifying the H2H^2 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.

Keywords

Cite

@article{arxiv.1205.2458,
  title  = {A method for deriving hypergeometric and related identities from the $H^2$ Hardy norm of conformal maps},
  author = {Greg Markowsky},
  journal= {arXiv preprint arXiv:1205.2458},
  year   = {2012}
}