Results 21 to 30 of about 1,331 (75)

Discrete orthogonality of hypergeometric polynomial sequences on linear and quadratic lattices [PDF]

arXiv, 2022
We present a method to obtain weight functions associated with linear and quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional of the orthogonal polynomial sequences in the Askey scheme, with the exception of the Jacobi, Bessel, Laguerre, and Hermite polynomials.
arxiv  

A note on monotonicity property of Bessel functions

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 561-566, 1997., 1997
A theorem of Lorch, Muldoon and Szegö states that the sequence is decreasing for α > −1/2, where Jα(t) the Bessel function of the first kind order α and jα,k its kth positive root. This monotonicity property implies Szegö′s inequality , when α ≥ α′ and α′ is the unique solution of .
Stamatis Koumandos
wiley   +1 more source

Fourier transform of hn(x + p)hn(x − p)

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 613-615, 1997., 1996
We evaluate Fourier transform of a function with Hermite polynomials involved. An elementary proof is based on a combinatorial formula for Hermite polynomials.
Mourad E. H. Ismail, Krzystztof Stempak
wiley   +1 more source

Transformations of certain generalized Kampé de Fériet functions II

International Journal of Stochastic Analysis, Volume 10, Issue 3, Page 297-304, 1997., 1996
The development of identities of multivariable hypergeometric functions is further extended based upon the methods of the previous study (H. Exton, J. Phys. A29 (1996), 357‐363) these functions occur in various applications in the fields of physics and quantum chemistry.
Harold Exton
wiley   +1 more source

Generating new classes of orthogonal polynomials

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 643-656, 1996., 1994
Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi‐definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence to be orthogonal. In particular, we can find explicitly the linear functional v such that the new sequence is the corresponding family of orthogonal
Amílcar Branquinho, Francisco Marcellán   +1 more
wiley   +1 more source

Umbral Methods and Harmonic Numbers

Axioms, 2018
The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli, Bruna Germano, Silvia Licciardi, Maria Renata Martinelli   +3 more
doaj   +1 more source

New generating functions for multivariate biorthogonal polynomials on the N‐sphere

International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 85-90, 1995., 1994
Certain multivariate biorthogonal polynomials on the N‐sphere arise in connection with quantum chromodynamics. These functions can be expressed in terms of Lauricella functions of the first kind, and multi‐dimensional generating functions for them are deduced by means of an extension of Bailey′s theorem.
Harold Exton
wiley   +1 more source

Some extensions of Bateman′s product formulas for the Jacobi polynomials

International Journal of Stochastic Analysis, Volume 8, Issue 4, Page 423-428, 1995., 1995
The authors derive generalizations of some remarkable product formulas of Harry Bateman (1882‐1946) for the classical Jacobi polynomials. They also show how the results considered here would lead to various families of linear, bilinear, and bilateral generating functions for the Jacobi and related polynomials.
Ming-Po Chen, H. M. Srivastava
wiley   +1 more source

Approximation by Phillips operators via q-Dunkl generalization based on a new parameter

Journal of King Saud University: Science, 2021
In the present article we study the approximation properties of Phillips operators by q-Dunkl generalization. We construct the operators in a new q-Dunkl form and obtain the approximation properties in weighted function space.
Abdullah Alotaibi, Md. Nasiruzzaman, M. Mursaleen   +2 more
doaj  

On Laguerre-Sobolev matrix orthogonal polynomials

Open Mathematics
In this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson, Garza Luis E., Saiz Martha L.   +2 more
doaj   +1 more source