Results 261 to 270 of about 58,842 (311)

Discrete classical orthogonal polynomials

Journal of Difference Equations and Applications, 1998
We find necessary and sufficient conditions for the difference equation of hypergeometric type to have polynomial solutions , which are orthogonal, that is Traditionallydμ(x) is a positive measure but here we allow it to be a signed measure. We then show that the usual restrictions on parameters in discrete classical orthogonal polynomials can be ...
Kwon, KH Kwon, Kil Hyun, Lee, DW, Park, SB, Yoo, BH   +3 more
openaire   +1 more source

Classical Continuous Orthogonal Polynomials

2020
Classical orthogonal polynomials (Hermite, Laguerre, Jacobi and Bessel) constitute the most important families of orthogonal polynomials. They appear in mathematical physics when Sturn-Liouville problems for hypergeometric differential equation are studied. These families of orthogonal polynomials have specific properties. Our main aim is to: 1.
openaire   +1 more source

On the Orthogonality of Classical Orthogonal Polynomials

Integral Transforms and Special Functions, 2003
We consider the orthogonality of rational functions W n ( s ) as the Laplace transform images of a set of orthoexponential functions, obtained from the Jacobi polynomials, and as the Laplace transform images of the Laguerre polynomials. We prove that the orthogonality of the Jacobi and the Laguerre polynomials is induced by the orthogonality of the ...
Slobodan TriČkoviĆ, Miomir StankoviĆ
openaire   +1 more source

Stieltjes’ theorem for classical discrete orthogonal polynomials

, 2020
The purpose of this note is to establish, from the hypergeometric-type difference equation introduced by Nikiforov and Uvarov, new tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical discrete ...
K. Castillo, F. R. Rafaeli, A. Suzuki
semanticscholar   +1 more source

The Classical Orthogonal Polynomials

1988
In §2 we introduced the polynomials y n (z) of hypergeometric type, which are solutions of $$\sigma \left( z \right)y'' + \tau \left( z \right)y' + \lambda y = 0$$ (1) with \(\lambda = {\lambda _n} = - n\tau ' - \frac{1}{2}n\left( {n - 1} \right)\sigma ''\)
Arnold F. Nikiforov, Vasilii B. Uvarov
openaire   +1 more source

Mitigating peak side-lobe levels in pulse compression radar using classical orthogonal polynomials

Wireless networks, 2022
Ankur Thakur, D. Saini
semanticscholar   +1 more source

Classical Orthogonal Polynomials

1999
Example 7.2.5 discussed only one of the many types of the so-called classical orthogonal polynomials. Historically, these polynomials were discovered as solutions to differential equations arising in various physical problems. Such polynomials can be produced by starting with 1,x,x 2,… and employing the Gram-Schmidt process.
openaire   +1 more source

On Three Families of Karhunen–Loève Expansions Associated with Classical Orthogonal Polynomials

Results in Mathematics, 2021
J. Pycke
semanticscholar   +1 more source

Gibbs phenomena for some classical orthogonal polynomials

, 2022
John M. Davis, P. Hagelstein
semanticscholar   +1 more source

The Dω—classical orthogonal polynomials

Results in Mathematics, 1997
This is an expository paper; it aims to give an essentially self-contained overview of discrete classical polynomials from their characterizations by Hahn’s property and a Rodrigues’ formula which allows us to construct it. The integral representations of corresponding forms are given.
F. Abdelkarim, P. Maroni
openaire   +1 more source