Results 41 to 50 of about 351,291 (192)
CHARACTERIZATION OF POLYNOMIALS VIA A RAISING OPERATOR
Проблемы анализа, 2023 This paper investigates a first-order linear differential operator 𝒥𝜉, where 𝜉 = (𝜉1, 𝜉2)\in (C^2\(0,0), and 𝐷 := 𝑑/𝑑𝑥. The operator is defined as 𝒥𝜉 := 𝑥(𝑥𝐷+ I) + 𝜉1 I + 𝜉2𝐷, with I representing the identity on the space of polynomials with complex ...
Jihad Souissi
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$q$-Classical orthogonal polynomials: A general difference calculus approach
, 2009 It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator.
A.F. Nikiforov +26 more
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The relation of the d-orthogonal polynomials to the Appell polynomials [PDF]
, 1996 We are dealing with the concept of d-dimensional orthogonal (abbreviated d-orthogonal) polynomials, that is to say polynomials verifying one standard recurrence relation of order d + 1.
Douak, Khalfa
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Curvilinearity and Orthogonality [PDF]
arXiv, 2022 We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal ...
arxiv
Krylov complexity and orthogonal polynomials
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
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Generalization of matching extensions in graphs—combinatorial interpretation of orthogonal and q-orthogonal polynomials [PDF]
, 2005 In this paper, we present generalization of matching extensions in graphs and we derive combinatorial interpretation of wide classes of orthogonal and q-orthogonal polynomials. Specifically, we assign general weights to complete graphs, cycles and chains
Kyriakoussis, A., Vamvakari, M.G.
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Classical orthogonal polynomials: dependence of parameters
Journal of Computational and Applied Mathematics, 2000 AbstractMost of the classical orthogonal polynomials (continuous, discrete and their q-analogues) can be considered as functions of several parameters ci. A systematic study of the variation, infinitesimal and finite, of these polynomials Pn(x,ci) with respect to the parameters ci is proposed.
A. Zarzo +3 more
openaire +3 more sources
A NEW CHARACTERIZATION OF 𝑞-CHEBYSHEV POLYNOMIALS OF THE SECOND KIND
Проблемы анализаIn this work, we introduce the notion of $\cal{U}_{(q, \mu)}$-classical orthogonal polynomials, where $\cal{U}_{(q, \mu)}$ is the degree raising shift operator defined by $\cal{U}_{(q, \mu)}$ $:= x(xH_q + q^{-1}I_{\cal{P}}) + \mu H_q$, where $\mu$ is a
S. Jbeli
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The orthogonal polynomials generated by [ceteris omissis] [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1995 Starting from the generating function, a differential-recurrence relation is derived, which is then combined with the three-term pure recurrence formula (a necessary and sufficient condition for orthogonal polynomials) to obtain a differential ...
A.L.W. VON BACHHAUS
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New Formulas and Connections Involving Euler Polynomials
Axioms, 2022 The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well
Waleed Mohamed Abd-Elhameed +1 more
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