منابع مشابه
Exceptional Meixner and Laguerre orthogonal polynomials
Using Casorati determinants of Meixner polynomials (m n )n , we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials ma,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials...
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It has been recently discovered that exceptional families of SturmLiouville orthogonal polynomials exist, that generalize in some sense the classical polynomials of Hermite, Laguerre and Jacobi. In this paper we show how new families of exceptional orthogonal polynomials can be constructed by means of multiple-step algebraic Darboux transformations. The construction is illustrated with an examp...
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We present various results on the properties of the four infinite sets of the exceptional X` polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414–417; Phys. Lett. B 684 (2010), 173–176]. These X` polynomials are global solutions of second order Fuchsian differential equations with ` + 3 regular singularities and their confluent limits. We derive equivalent but much...
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We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms, generating functions, and absolutely continuous part of the spectral measures are given. We derive fourth-order differential equations satisfied by the polynomials wi...
متن کاملLaguerre-type Bell polynomials
We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...
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ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2018
ISSN: 0022-2526
DOI: 10.1111/sapm.12204