Results 31 to 40 of about 2,557 (239)
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 +3 more
doaj +1 more source
Mathematics, 2018 In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds.
Taekyun Kim +3 more
doaj +1 more source
Advances in Difference Equations, 2019 In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials ...
Taekyun Kim +3 more
doaj +1 more source
Connection Problem for Sums of Finite Products of Legendre and Laguerre Polynomials [PDF]
Symmetry, 2019 The purpose of this paper is to represent sums of finite products of Legendre and Laguerre polynomials in terms of several orthogonal polynomials. Indeed, by explicit computations we express each of them as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, some of which involve terminating hypergeometric
Taekyun Kim 0001 +3 more
openaire +1 more source
An embedding of the universal Askey–Wilson algebra into Uq(sl2)⊗Uq(sl2)⊗Uq(sl2)
Nuclear Physics B, 2017 The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra Uq(sl2). In this paper, we display an injection of a universal analog △q of Askey–Wilson algebras into Uq(sl2)⊗Uq(sl2)⊗
Hau-Wen Huang
doaj +1 more source
Advances in Difference Equations, 2019 The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim +3 more
doaj +1 more source
Sum and Shifted-Product Subsets of Product-Sets over Finite Rings [PDF]
The Electronic Journal of Combinatorics, 2012 For sufficiently large subsets $\mathcal{A}, \mathcal{B}, \mathcal{C}, \mathcal{D}$ of $\mathbb{F}_q$, Gyarmati and Sárközy (2008) showed the solvability of the equations $a + b= c d$ and $a b + 1 = c d$ with $a \in \mathcal{A}$, $b \in\mathcal{B}$, $c \in \mathcal{C}$, $d \in \mathcal{D}$.
openaire +2 more sources
Sum-product estimates in finite fields
, 2006 We prove, using combinatorics and Kloosterman sum technology that if $A \subset {\Bbb F}_q$, a finite field with $q$ elements, and $q^{1/2} \lesssim |A| \lesssim q^{7/10}$, then $\max \{|A+A|, |A \cdot A|\} \gtrsim \frac{{|A|}^{3/2}}{q^{1/4}$.
Hart, D., Iosevich, A., Solymosi, J.
openaire +2 more sources
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective To explore how cerebral hypoxia and Normal‐Appearing White Matter (NAWM) integrity affect MS lesion burden and clinical course. Methods Seventy‐nine MS patients, including 13 clinically isolated syndrome (CIS) patients and 66 relapsing–remitting multiple sclerosis (RRMS) patients, and 44 healthy controls (HCs) were recruited from ...
Xinli Wang +8 more
wiley +1 more source
ON THE SOLVABILITY OF SYSTEMS OF SUM–PRODUCT EQUATIONS IN FINITE FIELDS [PDF]
Glasgow Mathematical Journal, 2011 AbstractIn an earlier paper, for ‘large’ (but otherwise unspecified) subsets , , , of q, Sárközy showed the solvability of the equations a + b = cd with a ∈ , b ∈ , c ∈ , d ∈ . This equation has been studied recently by many other authors. In this paper, we study the solvability of systems of equations of this type using additive character sums.
openaire +1 more source