Results 21 to 30 of about 7,643 (187)
Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials
Mathematics, 2020 In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and ...
Taekyun Kim +3 more
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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials [PDF]
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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FINITE SUMS THAT INVOLVE RECIPROCALS OF PRODUCTS OF GENERALIZED FIBONACCI NUMBERS
Integers, 2014 In this paper we find closed forms for certain finite sums. In each case the denominator of the summand consists of products of generalized Fibonacci numbers. Furthermore, we express each closed form in terms of rational numbers.
R. S. Melham
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Sums of finite products of Pell polynomials in terms of hypergeometric functions [PDF]
Journal of the Egyptian Mathematical Society, 2022 In this work, we study sums of finite products of Pell polynomials and express them in terms of some special orthogonal polynomials. Furthermore, each of the obtained expression is represented as linear combinations of classical polynomials involving ...
A. Patra, G. K. Panda
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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
Ding Xuan-hao
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Sums of finite products of Chebyshev polynomials of two different types
AIMS Mathematics, 2021 In this paper, we consider sums of finite products of the second and third type Chebyshev polynomials, those of the second and fourth type Chebyshev polynomials and those of the third and fourth type Chebyshev polynomials, and represent each of them as ...
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 ...
Taekyun Kim +3 more
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The Sum and Product of Finite Sequences of Complex Numbers [PDF]
Formalized Mathematics, 2010 The Sum and Product of Finite Sequences of Complex Numbers This article extends the [10]. We define the sum and the product of the sequence of complex numbers, and formalize these theorems. Our method refers to the [11].
Keiichi Miyajima, Takahiro A. Kato
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Combined Properties of Finite Sums And Finite products near zero [PDF]
, 2017 It was proved that whenever N is partitioned into finitely many cells, one cell must contain arbitrary length geo-arithmetic progressions. It was also proved that arithmetic and geometric progressions can be nicely intertwined in one cell of partition, whenever N is partitioned into finitely many cells. In this article we shall prove that similar types
Tanushree Biswas
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Sum-Product Type Estimates for Subsets of Finite Valuation Rings [PDF]
Acta Arithmetica, 2017 Let $R$ be a finite valuation ring of order $q^r.$ Using a point-plane incidence estimate in $R^3$, we obtain sum-product type estimates for subsets of $R$. In particular, we prove that for $A\subset R$, $$|AA+A|\gg \min\left\{q^{r}, \frac{|A|^3}{q^{2r-1}}\right\}.$$ We also show that if $|A+A||A|^{2}>q^{3r-1}$, then $$|A^2+A^2||A+A|\gg q^{\frac{r ...
Esen Aksoy Yazici
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