Results 71 to 80 of about 441,925 (264)

Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

Mathematics, 2019
In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials.
Dae San Kim, Dmitry V. Dolgy, Dojin Kim, Taekyun Kim   +3 more
doaj   +1 more source

Some identities involving Gegenbauer polynomials [PDF]

Advances in Difference Equations, 2012
11 ...
Seog-Hoon Rim, Dae San Kim, Taekyun Kim
openaire   +3 more sources

Weighted $$L^2$$-norms of Gegenbauer polynomials [PDF]

Aequationes mathematicae, 2022
We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{( )}(x))^2(1-x)^ (1+x)^ \, dx, \end{equation*} where $C_n^{( )}$ denotes the Gegenbauer-polynomial of index $ >0$ and $ , >-1$. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as $n\to\infty$.
Johann S. Brauchart, Peter J. Grabner
openaire   +2 more sources

Conformal string operators and evolution of skewed parton distributions [PDF]

, 1999
We have investigated skewed parton distributions in coordinate space. We found that their evolution can be described in a simple manner in terms of non-local, conformal operators introduced by Balitsky and Braun.
Balitskii, Balitsky, Belitsky, Belitsky, Belitsky, Blümlein, Braun, Brodsky, Brodsky, Carlson, Chase, Chase, Collins, Crittenden, Del Duca, Efremov, Efremov, Efremov, Erdelyi, Frankfurt, Frankfurt, Golec-Biernat, Gradshteyn, Gribov, Guichon, Hoodbhoy, Hoyer, Ioffe, Ioffe, Ioffe, Ji, Ji, Ji, Kantorovich, L. Mankiewicz, Makeenko, Mankiewicz, Mankiewicz, Mankiewicz, Mankiewicz, N. Kivel, Ohrndorf, Pestieau, Radyushkin, Radyushkin, Ryskin, van der Steenhoven, Vanderhaeghen, Vänttinen   +48 more
core   +2 more sources

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source

Fekete-Szegö Functional Problem for Analytic and Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

Contemporary Mathematics
This article aims to introduce a new qualitative subclass of bi-univalent and analytic functions that are intricately linked to Gegenbauer polynomials. These polynomials, known for their significant role in various areas of mathematics, provide a robust ...
Omar Alnajar, A. Amourah, J. Salah, M. Darus   +3 more
semanticscholar   +1 more source

A model for the continuous q-ultraspherical polynomials

, 1995
We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q ...
Askey R. A., Floreanini R., Luc Vinet, Rahman M., Roberto Floreanini   +4 more
core   +2 more sources

New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q-Srivastava-Attiya Operator

Mathematics, 2022
In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family JΣ(λ,γ,s,t,q;h) of holomorphic and bi-univalent functions which were defined in the unit disk D associated with the q-Srivastava–Attiya operator.
A. Wanas, Luminița-Ioana Cotîrlă
semanticscholar   +1 more source

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

, 2006
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer ...
Aizawa N Chakrabarti R Naina Mohammed S S Segar J, Askey R, Erdélyi A, Gasper G, Kibler M, Odake S, R Chakrabarti, R Jagannathan, Raychev P P, S S Naina Mohammed   +9 more
core   +1 more source

A Survey on Orthogonal Polynomials from a Monomiality Principle Point of View

Encyclopedia
This survey highlights the significant role of exponential operators and the monomiality principle in the theory of special polynomials. Using operational calculus formalism, we revisited classical and current results corresponding to a broad class of ...
Clemente Cesarano, Yamilet Quintana, William Ramírez   +2 more
doaj   +1 more source