Results 11 to 20 of about 1,681 (245)
Asymptotic Computation of Classical Orthogonal Polynomials [PDF]
, 2021 Contribution to ...
A. Gil (Amparo) +2 more
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Communications, 2010 In applications of mathematics involving either the Laplace or the Helmholtz equation in spherical coordinates the associated Legendre equation occurs. Its solutions are called associated Legendre functions. They have some relations to classical Legendre
Vladimir Guldan, Mariana Marcokova
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Mathematics, 2023 This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogs of Pascal distributions on a legged star-like set.
Jorge Arvesú +1 more
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d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property.
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q-Hermite Polynomials and Classical Orthogonal Polynomials [PDF]
Canadian Journal of Mathematics, 1996 AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials ...
Berg, Christian, Ismail, Mourad E. H.
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On 2-orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, 1999 Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0.
Khalfa Douak
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SECOND STRUCTURE RELATION FOR THE DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Проблемы анализа, 2023 In this paper, we characterize the Dunkl-classical orthogonal polynomials by a second structure relation.
Y. Habbachi
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International Journal of Mathematics and Mathematical Sciences, 2000 We give explicitly the recurrence coefficients of a nonsymmetric semi-classical sequence of polynomials of class s=1. This sequence generalizes the Jacobi polynomial sequence, that is, we give a new orthogonal sequence {Pˆn(α,α+1)(x,μ)}, where μ is an ...
Mohamed Jalel Atia
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On an system of “classical” polynomials of simultaneous orthogonality
Journal of Computational and Applied Mathematics, 1996 Let \(Q_{\overline n}(x)\), \(\overline n=(n_1,n_2)\), be the system of polynomials of simultaneous orthogonality [see \textit{E. M. Nikishin} and \textit{V. N. Sorokin}: ``Rational approximations and orthogonality'' (Russian orig. 1988; Zbl 0718.41002; Engl. transl. 1991; Zbl 0733.41001)] with \(\Delta_1=[a;0]\), \(\Delta_2=[0;1] (-1\leq a-1)\).
Kaliaguine, V., Ronveaux, André
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials
Mathematics, 2019 In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim +3 more
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