scholarly journals Associated polynomials, spectral matrices and the bispectral problem

1999 ◽  
Vol 6 (2) ◽  
pp. 209-224 ◽  
Author(s):  
F. Alberto Grünbaum ◽  
Luc Haine
Keyword(s):  
Associated Polynomials ◽  
Bispectral Problem

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals The CMV Bispectral Problem

2016 ◽  
pp. rnw186
Author(s):  
Francisco Alberto Grünbaum ◽  
Luis Velázquez
Keyword(s):  
Bispectral Problem

scholarly journals Erratum to “The CMV Bispectral Problem”

2016 ◽  
pp. rnw228
Author(s):  
Francisco Alberto Grünbaum ◽  
Luis Velázquez
Keyword(s):  
Bispectral Problem

The Associated Ultraspherical Polynomials and their q-Analogues

1982 ◽  
Vol 34 (3) ◽  
pp. 718-736 ◽  
Author(s):  
Joaquin Bustoz ◽  
Mourad E. H. Ismail
Keyword(s):  
Orthogonal Polynomials ◽  
Positive Measure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Ultraspherical Polynomials ◽  
Associated Polynomials ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Precise Degree

A sequence of polynomials {Pn(x)} is orthogonal if Pn(x) is of precise degree n and there is a finite positive measure dμ such that1.1A necessary and sufficient condition for orthogonality [9] is that {Pn(x)} satisfies a three term recurrence1.2with1.3Given a sequence of orthogonal polynomials {Pn(x)} satisfying (1.2), the associated polynomials {Pn(γ)(x)}, γ > 0, are defined by1.4with P(γ)-1(x) = 0, P0(γ)(x) = 1, when An+γ and Bn+γ are well-defined.

scholarly journals Interlacing properties of zeros of associated polynomials

1995 ◽  
Vol 59 (1) ◽  
pp. 61-78 ◽  
Author(s):  
Franz Peherstorfer ◽  
Michael Schmuckenschläger
Keyword(s):  
Associated Polynomials
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