Linear combinations of d-orthogonal polynomials Articles uri icon

publication date

  • December 2017

start page

  • 2009

end page

  • 2038

issue

  • 5

volume

  • 42

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