AN INVERSION INTEGRAL FOR A GEGENBAUER TRANSFORMATION

Abstract

Iden ifiers: Gegenbauer polynomials, Legendre polynomials, Chebyshev polynomials. T Li, a new class of integral transforms, obtained an integral inversion formula for an integral transformation where the kernel involved a Chebyshev polynomial of the first kind, and more recently Buschman obtained the integral inversion formula for a similar integral transformation where the kernel is a Legendre polynomial. An integral inversion formula is established for an integral transformation which contains the Gegenbauer polynomial in the kernel. The transforms obtained by Li and Buschman are both special cases of this transform pair. The general integral equation given here can always be inverted by an integral which involves Legendre polynomials or by one which involves Chebyshev polynomials. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1962
Accession Number
AD0293456

Entities

People

  • Theodore P. Higgins

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Chebyshev Polynomials
  • Equations
  • Integral Equations
  • Integral Transforms
  • Integrals
  • Inversion
  • Mathematical Analysis
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
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