منابع مشابه
Inequalities for Weierstrass Products
The aim of this note is to find new inequalities for the Weierstrass products n ∏
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We present the asymptotic expansions of functions involving the ratio of gamma functions and provide formulas for determining the coefficients of the asymptotic expansions. As consequences, we obtain the asymptotic expansions of the Wallis sequence. Also, we establish inequalities for the Wallis sequence.
متن کاملOn Wallis-type Products and Pólya's Urn Schemes
A famous “curious identity” of Wallis gives a representation of the constant π in terms of a simply structured infinite product of fractions. Sondow and Yi [Amer. Math. Monthly 117 (2010), 912-917] identified a general scheme for evaluating Wallis-type infinite products. The main purpose of this paper is to discuss an interpretation of the scheme by means of Pólya urn models.
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We establish several new inequalities of the constants of Landau and Lebesgue
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We study inequalities connecting the product of uniform norms of polynomials with the norm of their product. This circle of problems include the Gelfond-Mahler inequality for the unit disk and the KneserBorwein inequality for the segment [−1, 1]. Furthermore, the asymptotically sharp constants are known for such inequalities over arbitrary compact sets in the complex plane. It is shown here tha...
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ژورنال
عنوان ژورنال: Mathematica Moravica
سال: 2003
ISSN: 1450-5932,2560-5542
DOI: 10.5937/matmor0307067s