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

Tags

DTIC Thesaurus Topics

  • Convolution Integrals
  • Equations
  • Hypergeometric Functions
  • Integral Transforms
  • Integrals
  • Inverse Problems
  • Mathematical Analysis
  • Mathematics
  • Power Series

Fields of Study

  • Mathematics

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