THE COMBINATORY INTEGRAL TRANSFORM AND ITS APPLICATION TO HEUN'S EQUATION,
Abstract
The combinatory integral transforms mean the successive application of the Euler and the Laplace transforms in proper combination. Solutions to a certain class of Heun's equations and many classes of third order equations can be obtained through the use of the combinatory transform. Several properties of the Euler and the Laplace integral transforms are developed in Sections 2 and 3. The combinatory transform is studied in Section 4. The application of this transform in solving a Heun's equation is demonstrated in Section 5. The integral representation of the solution to a particular Heun's equation can be expanded as a power series of the hypergeometric functions, which may be compared with the one obtained by Erdelyi.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1964
- Accession Number
- AD0606090
Entities
People
- H. H. Chiu
- S. I. Cheng
Organizations
- Princeton University