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Asymptotics for some -hypergeometric polynomials
Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We tackle the study of a type of local asymptotics, known as Mehler--Heine asymptotics, for some --hypergeometric polynomials. Some consequences about the asymptotic behavior of…
Differential system related to Krawtchouk polynomials: iterated regularisation and Painlevé equation
Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar +1
We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities invol…
Characterization of Orthogonal Polynomials on lattices
D. Mbouna, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We consider two sequences of orthogonal polynomials and such that $$ \sum_{j=1} ^{M} a_{j,n}\mathrm{S}_x\mathrm{D}_x ^k P_{k+n-j} (z)=\sum_{j=1}…
Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials
Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators and and, as…
Classical Sobolev orthogonal polynomials: eigenvalue problem
Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
We consider the discrete Sobolev inner product where is a c…
Differential operator for discrete Gegenbauer--Sobolev orthogonal polynomials: eigenvalues and asymptotics
Lance L. Littlejohn, Juan F. Mañas-Mañas, Juan J. Moreno--Balcázar +1
We consider the following discrete Sobolev inner product involving the Gegenbauer weight $$(f,g)_S:=\int_{-1}^1f(x)g(x)(1-x^2)^αdx+M\big[f^{(j)}(-1)g^{(j)}(-1)+f^{(j)}(1)g^{(j)}(1)…