THE FINITE STURM-LIOUVILLE TRANSFORM

Abstract

Special transforms whose intervals are finite are unified and extended. A kernel is employed which may be determined to suit each particular type of problem. The Sturm-Liousville expansion is obtained for f(x) when f(x) is an integral function over (a,b) and a alxlb. The finite Sturm-Liouville transform is defined. Solutions are ontianed for some partial differential equations. Consideration is given to spherical harmonics; Hermite and Tchebycheff polynomials; and Bessel, Mathieu, and Wittaker functions. A heat conduction problem for which the solution was not known was successfully solved.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1953
Accession Number
AD0017504

Entities

People

  • A. C. Eringen

Organizations

  • Illinois Institute of Technology

Tags

Communities of Interest

  • C4I
  • Counter IED
  • Ground and Sea Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Applied Mechanics
  • Army
  • Differential Equations
  • Engineering
  • Engineers
  • Equations
  • Materials Laboratories
  • Mathematics
  • Mechanical Engineering
  • Mechanics
  • Munitions
  • New York
  • Ordnance Laboratories
  • Partial Differential Equations
  • Polynomials
  • Underwater Ordnance

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra