The complementary polynomials and the Rodrigues operator of classical orthogonal polynomials Articles uri icon

publication date

  • October 2012

start page

  • 3485

end page

  • 3493

issue

  • 10

volume

  • 140

international standard serial number (ISSN)

  • 0002-9939

electronic international standard serial number (EISSN)

  • 1088-6826

abstract

  • From the Rodrigues representation of polynomial eigenfunctions of a second order linear hypergeometric-type differential (difference or q-difference) operator, complementary polynomials for classical orthogonal polynomials are constructed using a straightforward method. Thus a generating function in a closed form is obtained. For the complementary polynomials we present a second order linear hypergeometric-type differential (difference or q-difference) operator, a three-term recursion and Rodrigues formulas which extend the results obtained by H.,I. Weber for the standard derivative operator.