82,268 research outputs found
Automorphisms of algebras and Bochner`s property for discrete vector orthogonal polynomials
We construct new families of discrete vector orthogonal polynomials that have
the property to be eigenfunctions of some difference operator. They are
extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas
behind our approach lie in the studies of bispectral operators. We exploit
automorphisms of associative algebras which transform elementary (vector)
orthogonal polynomial systems which are eigenfunctions of a difference operator
into other systems of this type. While the extension of Charlier polynomilas is
well known it is obtained by different methods. The extension of Meixner
polynomial system is new.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1512.0389
Bibliography: Publications of J. L. Doob
Publications of J. L. DoobComment: Compiled by Don Burkholder; Published in at
http://dx.doi.org/10.1214/09-AOP466 the Annals of Probability
(http://www.imstat.org/aop/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
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