Results 21 to 30 of about 2,569 (239)
A Few Finite Trigonometric Sums
Mathematics, 2017 Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products
Chandan Datta, Pankaj Agrawal
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The large N limit of SU(N) integrals in lattice models
Nuclear Physics B, 2020 The standard U(N) and SU(N) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of SU(N) models and discuss implications of
O. Borisenko, V. Chelnokov, S. Voloshyn
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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
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An improved sum-product estimate for general finite fields [PDF]
SIAM Journal on Discrete Mathematics, 2011 An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{|A+A|,|A·A|}≫|A|12/11(log2|A|)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev.
Liangpan Li, Oliver Roche-Newton
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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
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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
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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
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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
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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
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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 $a \in \mathcal{A}$, $b \in\mathcal{B}$, $c \in \mathcal{C}$, $d \in \mathcal{D}$.
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