When do Linear Combinations of Orthogonal Polynomials Yield New Sequences of Orthogonal Polynomials? Articles uri icon

publication date

  • January 2010

start page

  • 1446

end page

  • 1452


  • 6


  • 233

International Standard Serial Number (ISSN)

  • 0377-0427

Electronic International Standard Serial Number (EISSN)

  • 1879-1778


  • Given {P"n}"n">="0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,
    Necessary and sufficient conditions are given for the orthogonality of
    the sequence {Q"n}"n">="0. An interesting interpretation in terms of
    the Jacobi matrices associated with {P"n}"n">="0 and {Q"n}"n">="0
    is shown. Moreover, in the case k=2, we characterize the families
    {P"n}"n">="0 such that the corresponding polynomials {Q"n}"n">="0
    are also orthogonal.