منابع مشابه
Diophantus and the Arithmetica
“Knowing, my most esteemed friend Dionysius, that you are anxious to learn how to investigate problems in numbers, I have tried, beginning from the foundations on which the science is built up, to set forth to you the nature and power subsisting in numbers.” Thus Diophantus begins his great work Arithmetica (Heath, 129) and gives the world what would become its most ancient text on algebra. The...
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(1) f(x) = x+o(x) . The problem is discussed explicitly by Landau ([7], pp . 597-604 ; [8]), Ingham ([3]), Karamata ([5], [6]), Gordon ([1]), and is implicit in the 'Eratosthenian' summation method introduced by Wintner ([10], [11]) . In this paper we consider the analogous problem in which the sequence {n} of all positive integers is replaced by a finite or infinite sequence 1, a,, a2, . . . o...
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The present note generalizes Wallis’ formula, 2 = . 7 6 . 5 6 . 5 4 . 3 4 . 3 2 . 1 2 , using the EulerMascheroni constant g and the Glaisher-Kinkelin constant A: 2 ln 2 4 = 3 3 2 . 1 2 . 5 4 3 4
متن کاملWallis-Ramanujan-Schur-Feynman
One of the earliest examples of analytic representations for π is given by an infinite product provided by Wallis in 1655. The modern literature often presents this evaluation based on the integral formula 2 π ∫ ∞ 0 dx (x + 1) = 1 2 (
متن کاملThe John–Nirenberg inequality with sharp constants Meilleures constantes dans l’inégalité de John–Nirenberg
Article history: Received 14 March 2013 Accepted after revision 3 July 2013 Available online 29 July 2013 Presented by Yves Meyer We consider the one-dimensional John–Nirenberg inequality: ∣∣{x ∈ I0: ∣∣ f (x)− f I0 ∣∣>α}∣∣ C1|I0|exp ( − C2 ‖ f ‖∗ α ) . A. Korenovskii found that the sharp C2 here is C2 = 2/e. It is shown in this paper that if C2 = 2/e, then the best possible C1 is C1 = 2 e4/e. ©...
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ژورنال
عنوان ژورنال: Boletim Cearense de Educação e História da Matemática
سال: 2018
ISSN: 2447-8504,2357-8661
DOI: 10.30938/bocehm.v5i14.229