Some boundary value problems associated with the Heun equation
In this thesis an attempt has been made to complete to a large extent one's knowledge of the solutions of the Heun equation. After the formulation of the equation and a discussion of the convergence of the power series solutions, a new notation is introduced, (Chapter 1). In Chapter 2 integ...
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University of Surrey
1966
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ndltd-bl.uk-oai-ethos.bl.uk-7516612018-10-09T03:27:05ZSome boundary value problems associated with the Heun equationSleeman, Brian David1966In this thesis an attempt has been made to complete to a large extent one's knowledge of the solutions of the Heun equation. After the formulation of the equation and a discussion of the convergence of the power series solutions, a new notation is introduced, (Chapter 1). In Chapter 2 integral representations of the solutions of Heun's equation are discussed. Chapter 3 is concerned with certain orthogonality properties, while Chapter 4 deals with new non-linear integral equations satisfied by Heun functions and Heun polynomials. In Chapter 5 Lame's equation is discussed as a special case of Heim's equation. The objective of this chapter is to correct the statement that Lame functions of the second kind associated with the Lame polynomials can be expressed as a finite series of associated Legendre functions of the second kind. In Appendices A and B the work of two previous investigations is summarized.University of Surreyhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751661http://epubs.surrey.ac.uk/848314/Electronic Thesis or Dissertation |
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NDLTD |
| description |
In this thesis an attempt has been made to complete to a large extent one's knowledge of the solutions of the Heun equation. After the formulation of the equation and a discussion of the convergence of the power series solutions, a new notation is introduced, (Chapter 1). In Chapter 2 integral representations of the solutions of Heun's equation are discussed. Chapter 3 is concerned with certain orthogonality properties, while Chapter 4 deals with new non-linear integral equations satisfied by Heun functions and Heun polynomials. In Chapter 5 Lame's equation is discussed as a special case of Heim's equation. The objective of this chapter is to correct the statement that Lame functions of the second kind associated with the Lame polynomials can be expressed as a finite series of associated Legendre functions of the second kind. In Appendices A and B the work of two previous investigations is summarized. |
| author |
Sleeman, Brian David |
| spellingShingle |
Sleeman, Brian David Some boundary value problems associated with the Heun equation |
| author_facet |
Sleeman, Brian David |
| author_sort |
Sleeman, Brian David |
| title |
Some boundary value problems associated with the Heun equation |
| title_short |
Some boundary value problems associated with the Heun equation |
| title_full |
Some boundary value problems associated with the Heun equation |
| title_fullStr |
Some boundary value problems associated with the Heun equation |
| title_full_unstemmed |
Some boundary value problems associated with the Heun equation |
| title_sort |
some boundary value problems associated with the heun equation |
| publisher |
University of Surrey |
| publishDate |
1966 |
| url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.751661 |
| work_keys_str_mv |
AT sleemanbriandavid someboundaryvalueproblemsassociatedwiththeheunequation |
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