Results 61 to 70 of about 351,291 (192)

Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials

Mathematics, 2018
This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon, Dmitry V. Dolgy   +3 more
doaj   +1 more source

The Kontorovich-Lebedev transform as a map between $d$-orthogonal polynomials

, 2012
A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this $KL_{\alpha}$-transform over certain polynomial sequences will be under discussion, and a special attention will be given
Appell, Atakishiyeva, Cheikh, Cheikh, Cheikh, Chihara, Douak, Erdélyi, Gornevelt, Iseghem, Ismail, Koelink, Koornwinder, Koornwinder, Lebedev, Loureiro, Loureiro, Loureiro, Maroni, Maroni, Maroni, Maroni, Maroni, Prudnikov, Prudnikov, Riordan, Sneddon, Srivastava, Toscano, Van Assche, Wimp, Yakubovich, Yakubovich, Yakubovich   +33 more
core   +1 more source

Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations [PDF]

in "Orthogonal Polynomials" (M. Foupouagnigni, W. Koepf, eds), Tutorials, Schools and Workshops in the Mathematical Sciences, Springer Nature Switzerland, 2020, pp. 629-683, 2019
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics and probability and many other disciplines.
arxiv   +1 more source

On moments of classical orthogonal polynomials

Journal of Mathematical Analysis and Applications, 2015
Abstract In this work, using the inversion coefficients and some connection coefficients between some polynomial sets, we give explicit representations of the moments of all the orthogonal polynomials belonging to the Askey–Wilson scheme. Generating functions for some of these moments are also provided.
P. Njionou Sadjang, M. Foupouagnigni, M. Foupouagnigni, Wolfram Koepf   +3 more
openaire   +2 more sources

Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

Advances in Mathematical Physics, 2018
Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
doaj   +1 more source

Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

Mathematics, 2021
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle.
Pedro Zamora, Alejandro Arceo, Noé Martínez, Gerardo Romero, Luis E. Garza   +4 more
doaj   +1 more source

A basic class of symmetric orthogonal polynomials of a discrete variable [PDF]

, 2012
By using a generalization of Sturm-Liouville problems in discrete spaces, a basic class of symmetric orthogonal polynomials of a discrete variable with four free parameters, which generalizes all classical discrete symmetric orthogonal polynomials, is introduced.
arxiv   +1 more source

New characterizations of classical orthogonal polynomials

Indagationes Mathematicae, 1996
AbstractClassical orthogonal polynomials of Jacobi, Laguerre, Hermite, and Bessel are characterized as the only orthogonal polynomials (up to a linear change of variable) such that 1.(i) (Bochner) they satisfy a second order differential equation of the form l2(x)y″(x) + l1(x)y′(x) = λny(x); and2.(ii) (Hahn) their derivatives of any fixed order are ...
Kil Hyun Kwon, Kil Hyun Kwon, Kil Hyun Kwon, Lance L. Littlejohn, Lance L. Littlejohn, Lance L. Littlejohn, B. H. Yoo, B. H. Yoo, B. H. Yoo   +8 more
openaire   +3 more sources

Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials [PDF]

J. Math. Phys. 62, 013509 (2021), 2019
The discrete orthogonality relations hold for all the orthogonal polynomials obeying three term recurrence relations. We show that they also hold for multi-indexed Laguerre and Jacobi polynomials, which are new orthogonal polynomials obtained by deforming these classical orthogonal polynomials.
arxiv   +1 more source

On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices

Bulletin of Mathematical Sciences
Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation.
Misael E. Marriaga, Guillermo Vera de Salas, Marta Latorre, Rubén Muñoz Alcázar   +3 more
doaj   +1 more source