Results 21 to 30 of about 166,064,113 (263)
On Some Formulas for the Lauricella Function
Mathematics, 2023 Lauricella, G. in 1893 defined four multidimensional hypergeometric functions FA, FB, FC and FD. These functions depended on three variables but were later generalized to many variables.
Ainur Ryskan, Tuhtasin Ergashev
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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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THE FINITE SUM OF THE PRODUCTS OF TWO TOEPLITZ OPERATORS [PDF]
Journal of the Australian Mathematical Society, 2009 AbstractWe consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a
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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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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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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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A study in sums of products [PDF]
We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic ...
Michel, Philippe +2 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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