Results 21 to 30 of about 4,545,650 (236)
New BBP-Type Formulae for π Derived from New Forms of Taylor Expansions of Inverse Tangent Function
Mathematics, 2022 In this work, we give two new Taylor expansions of arctan(x + ω), where ω represents a finite increment of x. We discover several remarkable infinite series from these expansions by special substitutions.
Xin Wu, Zhongfan Chen, Yinan Zhu
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DIDACTIC VALUE OF MATHEMATICAL CONCEPT
Наука Красноярья, 2015 In article the didactic value of exact mathematical concept on the example of concepts of the section «Numerical Ranks» reveals. The definition of concept of a row specified in this article, fixes the real defining signs allowing to identify unambi ...
Elena Evgenevna Alekseeva
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Series of Floor and Ceiling Functions—Part II: Infinite Series
Mathematics, 2022 In this part of a series of two papers, we extend the theorems discussed in Part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, polylogarithms and Fibonacci ...
Dhairya Shah +4 more
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Infinite Series, Limits, Relationships and Aliasing
Brazilian Journal of Geophysics, 1995 This paper presents a coherent approach to the evaluation of limits of certaininfinife serieì and to the establishrnènt of relationships which exist between such series. The approach is based on the connection which exists between the Discrete
Tadeusz J. Ulrychl, Jacob T. Fokkema
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AppliedMathTwo classes of series involving differences of harmonic numbers and the binomial coefficients C(3n,n) are evaluated in closed form. The classes under consideration are ∑k=0∞H3k+1−Hk(3k+1)3kkkmzkand∑k=0∞H2k−Hk(3k+1)3kkkmzk, where z is a complex number and
Kunle Adegoke, Robert Frontczak
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Journal of Inequalities and Applications, 2017 In this paper, we established a generalized theorem on a minimal set of sufficient conditions for absolute summability factors by applying a sequence of a wider class (quasi-power increasing sequence) and the absolute Cesàro φ − | C , α , β ; δ | k ...
Smita Sonker, Alka Munjal
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Bivariate Infinite Series Solution of Kepler’s Equations
Mathematics, 2021 A class of bivariate infinite series solutions of the elliptic and hyperbolic Kepler equations is described, adding to the handful of 1-D series that have been found throughout the centuries.
Daniele Tommasini
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A new note on factored infinite series and trigonometric Fourier series
Comptes Rendus. Mathématique, 2021 In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series.
Bor, Hüseyin
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Tokyo Journal of Mathematics, 1993 It is well-known that the Riemann zeta function possesses the Laurent expansion \[ \zeta(s)={\textstyle {1\over {s-1}}}+ \sum_{n=0}^ \infty {\textstyle{{(-1)^ n} \over {n!}}} \nu(n) (s-1)^ n \] where \[ \nu(n)= \lim_{N\to\infty} \biggl\{ \sum_{k=1}^ N {{\log^ n k} \over k} - {{\log^{n+1} N} \over {n+1}} \biggr\}.
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Some infinite series identities
, 1993 Certain infinite series are shown to satisfy simple identities between the square of the sum of the series and the sum of the squares of the terms of the series. The main tool is Ramanujan’s 1
Kevin B. Ford
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