Results 21 to 30 of about 351,291 (192)
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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Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure [PDF]
, 2015 This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ?
Alfredo Deaño +28 more
core +6 more sources
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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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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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
Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations [PDF]
, 2016 The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere.
Martínez, Clotilde, Piñar, Miguel A.
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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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A conjecture on Exceptional Orthogonal Polynomials [PDF]
, 2012 Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López +42 more
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