Results 31 to 40 of about 411,141 (342)
On Semi-Classical Orthogonal Polynomials Associated with a Modified Sextic Freud-Type Weight
Mathematics, 2020 Polynomials that are orthogonal with respect to a perturbation of the Freud weight function by some parameter, known to be modified Freudian orthogonal polynomials, are considered. In this contribution, we investigate certain properties of semi-classical
A. Kelil, A. Appadu
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Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2021 This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying the Askey scheme, we explicitly construct the classical skew orthogonal ...
Bo-Jian Shen, Shi-Hao Li, Guo-Fu Yu
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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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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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Sums of finite products of Pell polynomials in terms of hypergeometric functions
Journal of the Egyptian Mathematical Society, 2022 In this work, we study sums of finite products of Pell polynomials and express them in terms of some special orthogonal polynomials. Furthermore, each of the obtained expression is represented as linear combinations of classical polynomials involving ...
Asim Patra, Gopal Krishna Panda
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Determinantal Formulas for Exceptional Orthogonal Polynomials [PDF]
SIGMA 18 (2022), 047, 16 pages, 2022 We present determinantal formulas for families of exceptional $X_m$-Laguerre and exceptional $X_m$-Jacobi polynomials and also for exceptional $X_2$-Hermite polynomials. The formulas resemble Vandermonde determinants and use the zeros of the classical orthogonal polynomials.
arxiv +1 more source
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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Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials [PDF]
SIGMA 19 (2023), 020, 18 pages, 2022 A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are ...
arxiv +1 more source
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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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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