Titlebook: Analytic Number Theory, Approximation Theory, and Special Functions; In Honor of Hari M. Gradimir V. Milovanović,Michael Th. Rassias Book

机警

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The Mean Values of the Riemann Zeta-Function on the Critical LineIn this overview we give a detailed discussion of power moments of .(.), when . lies on the “critical line” .. The survey includes early results, the mean square and mean fourth power, higher moments, conditional results and some open problems.

形容词

Explicit Bounds Concerning Non-trivial Zeros of the Riemann Zeta FunctionIn this paper, we get explicit upper and lower bounds for .., where . are consecutive ordinates of non-trivial zeros . of the Riemann zeta function. Meanwhile, we obtain the asymptotic relation . as . → ..

Expostulate

Identities for Reciprocal BinomialsEuler’s results related to the sum of the ratios of harmonic numbers and binomial coefficients are investigated in this paper. We give a particular example involving quartic binomial coefficients.

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A Note on ,-Stirling NumbersThe .-Stirling numbers of both kinds are specializations of the complete or elementary symmetric functions. In this note, we use this fact to prove that the .-Stirling numbers can be expressed in terms of the .-binomial coefficients and vice versa.

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A Survey on Cauchy–Bunyakovsky–Schwarz Inequality for Power SeriesIn this paper, we present a survey of some recent results for the celebrated Cauchy–Bunyakovsky–Schwarz inequality for functions defined by power series with nonnegative coefficients. Particular examples for fundamental functions of interest are presented. Applications for some special functions are given as well.

白杨鱼

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Expertise

https://doi.org/10.1007/978-1-4939-0258-3Analytic Number Theory; Approximation theory; Riemann Hypothesis; additive number theory; hypergeometric

影响带来

978-1-4939-4538-2Springer Science+Business Media New York 2014