Linear combinations of d-orthogonal polynomials Articles uri icon

publication date

  • December 2017

start page

  • 1

end page

  • 30

international standard serial number (ISSN)

  • 0126-6705

electronic international standard serial number (EISSN)

  • 2180-4206

abstract

  • The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when (r−1) is a multiple of d. This problem can be solved without the introduction of the concept of d-quasi-orthogonality. In the present contribution, we deal with the problem of d-orthogonality of a linear combination of two elements of a monic d-orthogonal polynomial sequence. This problem is also equivalent to the study the regularity of the left product of a linear form by a matrix polynomial of degree one.

keywords

  • d-Orthogonal polynomials; d-Dimensional vectors of linear forms; recurrence relations; Linear combinations of d-orthogonal polynomials; chebyshev d-orthogonal polynomials; associated and co-recursive d-orthogonal polynomials