Expansions in Legendre Functions of Integral Degree of Legendre Eigenfunctions of Non-integral Degree Arising in the Study of Stability of Incomplete Spherical Structures.

Abstract

It is shown that, if y(x) not identically equal to 0 satisfies Legendre's equation ((1-x square)y')' + n(n+1)y = 0 for x sub 0 < x < 1, -1 < x sub square < 1, n > 0 not integral, and the boundary conditions y(1) finite, y(x sub 0) = 0, then y(x) admits an explicit expansion of a particularly simple kind in the Legendre polynomials.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1974
Accession Number
ADA004467

Entities

People

  • Harry E. Rauch

Organizations

  • City University of New York

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Integrals
  • Legendre Functions
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Real Variables

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis