1,720,972 research outputs found
Relativistic Jacobi Polynomials
No full textA new polynomials set, of generalized hypergeometric type, is defined. These polynomials, called relativistic Jacobi polynomials (RJP) and denoted by
represent an extension of the classical Jacobi orthogonal polynomials in the sense that they reduce to the latter in the non-relativistic limit (N→ ∞). Some basic properties of these polynomials, as well as for the RHP (see [6] and [7]) and the RLP (see [2] and [3]), are derived
Eigenfunctions of Laguerre-type operators and generalized evolution problems
No full textWe consider eigenfunctions of a class of differential operators generalizing the Laguerre derivative. Applications in the framework of generalized evolution problems are also derived. © 2005 Elsevier Ltd. All rights reserved
Advanced special functions and solutions of PDEs. Seminario Interdisciplinare di Matematica
No full text
Zero's asymptotic distribution of polynomials orthogonal with respect to varying weights
No full textOn Taylor’s Formula for the Resolvent of a Complex Matrix
No full textThe resolvent Rλ(A) of a complex r×r matrix A is an analytic function in any domain with empty intersection with the spectrum ΣA of A. The well known Taylor expansion of Rλ(A) in a neighborhood of any given λ0∉ΣA is modified taking into account that only the first powers of Rλ0(A) are linearly independent. The main tool in this framework is given by the multivariable polynomials depending on the invariants v1,v2,…,vr of Rλ(A) (m denotes the degree of the minimal polynomial). These functions are used in order to represent the coefficients of the subsequent powers of Rλ0(A) as a linear combination of the first m of them
Differential Equations of Some Classes of Special Functions via the Factorization Method
No full textLet {P n(x)} n=0∞ be a sequence of polynomials of degree n. We define two sequences of differential operators Φ n and ψ n satisfying the following properties Φ n(P n(x))=P n-1(x), Ψ n(Pn(x)) = P n+1(x). By constructing these two operators for some classes of special functions, we determine their differential equations via the factorization method introduced in [3]. We illustrate our method by including classical orthogonal polynomials, d-orthogonal polynomials, confluent hypergeometric functions and hypergeometric functions as the applications. Copyright 2004 Eudoxus Press, LLC
The Relativistic Szego Polynomials
No full textA new relativistic-type polynomiasl system is defined by means of the Relativistic Polynomial (RLP) system
, recently introduced by P. Natalini. These polynomials, denoted by
, are called Relativistic Generalized Hermite Polynomials (RGHP) because they reduce, in the non-relativistc limit
, to the Generalized Hermite Polynomials first considered by G. Szegö. Some properties of this new set of orthogonal polynomials are derived
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