Chebyshev series expansions of the functions and
Z. Cylkowski (1966)
Applicationes Mathematicae
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Z. Cylkowski (1966)
Applicationes Mathematicae
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Roland Coghetto (2016)
Formalized Mathematics
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In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of [...] ℰTn and in [20] he has formalized that [...] ℰTn is second-countable, we build (in the topological sense defined in [23]) a denumerable base of [...] ℰTn . Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝn [16], semi-intervalle (borné) de ℝn [22]). We conclude with the definition of Chebyshev distance [11]. ...
Harold G. Diamond, Wen-Bin Zhang (2013)
Acta Arithmetica
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If the counting function N(x) of integers of a Beurling generalized number system satisfies both and , then the counting function π(x) of the primes of this system is known to satisfy the Chebyshev bound π(x) ≪ x/logx. Let f(x) increase to infinity arbitrarily slowly. We give a construction showing that and do not imply the Chebyshev bound.
Boaz Cohen (2021)
Czechoslovak Mathematical Journal
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We shall describe how to construct a fundamental solution for the Pell equation over finite fields of characteristic . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation .
Hacène Belbachir, Farid Bencherif (2008)
Discussiones Mathematicae - General Algebra and Applications
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Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
T. Bloom, L. Bos, N. Levenberg (2012)
Annales Polonici Mathematici
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We calculate the transfinite diameter for the real unit ball and the real unit simplex
Jean Schmets, Manuel Valdivia (2005)
Annales Polonici Mathematici
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We deal with projective limits of classes of functions and prove that: (a) the Chebyshev polynomials constitute an absolute Schauder basis of the nuclear Fréchet spaces ; (b) there is no continuous linear extension map from into ; (c) under some additional assumption on , there is an explicit extension map from into by use of a modification of the Chebyshev polynomials. These results extend the corresponding ones obtained by Beaugendre in [1] and [2].
T. Alden Gassert (2014)
Journal de Théorie des Nombres de Bordeaux
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Let be any integer and fix an odd prime . Let denote the -fold composition of the Chebyshev polynomial of degree shifted by . If this polynomial is irreducible, let , where is a root of . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on that ensure is monogenic. For other values of , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of and compute an integral basis for the ring...
Łukasz Piasecki (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The aim of this paper is to show that for every Banach space containing asymptotically isometric copy of the space there is a bounded, closed and convex set with the Chebyshev radius such that for every there exists a -contractive mapping with for any .
Swami Jnanananda (1936)
Časopis pro pěstování matematiky a fysiky
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S. B. Stechkin (1989)
Banach Center Publications
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M. K. Sen (1971)
Annales Polonici Mathematici
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A. Szymański (1977)
Colloquium Mathematicae
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P. Srivastava, K. K. Azad (1981)
Matematički Vesnik
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Janusz Matkowski (1989)
Annales Polonici Mathematici
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Ralph McKenzie (1971)
Colloquium Mathematicae
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Stephan Baier (2004)
Acta Arithmetica
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A. Pełczyński, H. Rosenthal (1975)
Studia Mathematica
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David Brink (2015)
Acta Arithmetica
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We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in...
А.М. Вершик (1972)
Zapiski naucnych seminarov Leningradskogo
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K. Orlov (1981)
Matematički Vesnik
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A. Makowski (1964)
Matematički Vesnik
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