Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T04:42:51.347Z Has data issue: false hasContentIssue false

4 - Elliptic Hypergeometric Functions

Published online by Cambridge University Press:  07 October 2020

By
Hjalmar Rosengren
Edited by
Howard S. Cohl  and
Mourad E. H. Ismail
Howard S. Cohl
Affiliation:
National Institute of Standards and Technology
Mourad E. H. Ismail
Affiliation:
University of Central Florida
Get access

Summary

The purpose of this chapter is to give an elementary introduction to the most fundamental aspects of elliptic hypergeometric functions. We will also give some indication of their historical origin in statistical mechanics. We will explain how elliptic hypergeometric functions can be used to construct biorthogonal rational functions, generalizing the famous Askey scheme of orthogonal polynomials. Apart from some general mathematical maturity, the only prerequisites will be elementary linear algebra and complex function theory.

Keywords

elliptic hypergeometric functionsbiorthogonal rational functionselliptic functionselliptic hypergeometric serieselliptic hypergeometric integralselliptic solid-on-solid model
Type
Chapter
Information
Lectures on Orthogonal Polynomials and Special Functions , pp. 213 - 279
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×