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 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}
}