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- W2950205870 abstract "Given a sequence of polynomials $(p_n)_n$, an algebra of operators $mathcal{A}$ acting in the linear space of polynomials and an operator $D_pin mathcal{A}$ with $D_p(p_n)=np_n$, we form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of $m$ consecutive $p_n$: $q_n=p_n+sum_{j=1}^mbeta_{n,j}p_{n-j}$. Using the concept of $mathcal{D}$-operator, we determine the structure of the sequences $beta_{n,j}, j=1,ldots,m,$ in order that the polynomials $(q_n)_n$ are common eigenfunctions of an operator in the algebra $mathcal{A}$. As an application, from the classical discrete families of Charlier, Meixner and Krawtchouk we construct orthogonal polynomials $(q_n)_n$ which are also eigenfunctions of higher order difference operators." @default.
- W2950205870 created "2019-06-27" @default.
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- W2950205870 date "2013-07-04" @default.
- W2950205870 modified "2023-10-01" @default.
- W2950205870 title "Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk" @default.
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