On Polar Legendre Polynomials Articles uri icon

publication date

  • May 2010

start page

  • 2025

end page

  • 2036


  • 6


  • 40

International Standard Serial Number (ISSN)

  • 0035-7596

Electronic International Standard Serial Number (EISSN)

  • 1945-3795


  • In this paper we introduce a new class of polynomials {Pn}, called polar Legendre polynomials. They appear as solutions of an inverse Gauss problem for the equilibrium position of a field of forces with n + 1 unit masses. We study algebraic, differential, and symptotic properties of these polynomials, which are simultaneously orthogonal with respect to a differential operator and discrete-continuous Sobolev type inner product.