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    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:
  • Published online: 01 January 2009

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.

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

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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