Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kalnins, E. G. and Miller, Jr., W. 1991. Addendum: Hypergeometric Expansions of Heun Polynomials. SIAM Journal on Mathematical Analysis, Vol. 22, Issue. 6, p. 1803.


    Schmidt, Dieter and Wolf, Gerhard 1979. A Method of Generating Integral Relations by the Simultaneous Separability of Generalized Schrödinger Equations. SIAM Journal on Mathematical Analysis, Vol. 10, Issue. 4, p. 823.


    Sleeman, B. D. 1972. Conference on the Theory of Ordinary and Partial Differential Equations.


    ×
  • Proceedings of the Edinburgh Mathematical Society, Volume 16, Issue 4
  • December 1969, pp. 281-289

Non-linear integral equations for Heun functions

  • B. D. Sleeman (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091500012943
  • Published online: 01 January 2009
Abstract

Some years ago Lambe and Ward (1) and Erdélyi (2) obtained integral equations for Heun polynomials and Heun functions. The integral equations discussed by these authors were of the form

Further, as is well known, the Heun equation includes, among its special cases, Lamé's equation and Mathieu's equation and so (1.1) may be considered a generalisation of the integral equations satisfied by Lamé polynomials and Mathieu functions. However, integral equations of the type (1.1) are not the only ones satisfied by Lamé polynomials; Arscott (3) discussed a class of non- linear integral equations associated with these functions. This paper then is concerned with discussing the existence of non-linear integral equations satisfied by solutions of Heun's equation.

    • Send article to Kindle

      To send this article 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 sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

      Non-linear integral equations for Heun functions
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and 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 Dropbox account. Find out more about sending content to Dropbox.

      Non-linear integral equations for Heun functions
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and 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 Google Drive account. Find out more about sending content to Google Drive.

      Non-linear integral equations for Heun functions
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(3) F. M. Arscott Integral equations and relations for Lamé functions, Quart. J. Math. Oxford ser. (2), 15 (1964), 103115.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×