A Generalization of Ultraspherical Polynomials.

Abstract

Some old polynomials of L. J. Rogers are orthogonal. Their weight function is given. The connection coefficient problem, which Rogers solved by guessing the formula and proving it by induction, is derived in a natural way and some other formulas are obtained. These polynomials generalize zonal spherical harmonics on spheres and include as special cases polynomials that are spherical functions on rank one spaces over reductive p-adic groups. A limiting case contains some Jacobi polynomials studied by Hylleraas that arose in work on the Yukawa potential. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1978
Accession Number
ADA060664

Entities

People

  • Mourad E.-h. Ismail
  • Richard Askey

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Binomials
  • Coefficients
  • Complex Variables
  • Distribution Functions
  • Functions (Mathematics)
  • Harmonics
  • Hypergeometric Functions
  • Identities
  • Mathematical Analysis
  • Mathematics
  • Orthogonality
  • Polynomials
  • Potential Theory
  • Spherical Harmonics
  • Theorems
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra

Technology Areas

  • Space
  • Space - Orbital Debris