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A Generalized Series Expansion of the Arctangent Function Based on the Enhanced Midpoint Integration
AppliedMath, 2023 In this work, we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a two-step iteration without surd or complex ...
Sanjar M. Abrarov +3 more
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Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2022 The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s).
Hüseyin Irmak
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An approach for one dimensional periodic arbitrary lithography based on Fourier series
Engineering Science and Technology, an International Journal, 2021 In interference lithography, 1-dimensional (1D) Fourier series expansion (FSE) technique can be used to create 1D periodic arbitrary patterns. Since the energy of electric field can change the solubility of photoresist, the required electric field ...
Mahdi Kordi +3 more
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, 2021 Viscoplasticity and pyroplasticity of clays are important characteristics to control in production processes of lightweight concrete aggregates. When clay is calcined under temperatures above 1,000 ℃, its volume increases.
Cáceres, J R +2 more
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Expansion of multiple series in infinite diagonals
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 In this paper a method of summation of double absolutely convergent numerical series was obtained. This method was named the expansion of double numerical series in infinite diagonals.
Anton A Korneev, Olga A Doroshkevich
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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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Asymptotic expansion of a series of Ramanujan [PDF]
Proceedings of the Edinburgh Mathematical Society, 1992 An asymptotic expansion is given for the seriesas x→∞ in the sector |Argx|≦π/2–δ. Here δ, Re(a), and Re(s) are positive and r is a positive integer. In the case a = r = s = 1, this yields the nontrivial resultstated by Ramanujan in his notebooks [6].
Berndt, Bruce C., Evans, Ronald J.
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SERIES EXPANSIONS AND SUDDEN SINGULARITIES [PDF]
The Thirteenth Marcel Grossmann Meeting, 2015 We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with a sudden singularity containing two free constants, as required for a general solution of the cosmological ...
Barrow, John D. +2 more
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The continued fraction expansion of certain Pierce series [PDF]
, 2017 A Pierce series is an alternating sum of the reciprocals of an increasing sequence of positive integers, each one divisible by the previous one. In this short note we study some Pierce series that arise from certain continued fractions. Moreover, we show
Varona, J.L. [0000-0002-2023-9946] +1 more
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Power series expansions for spheroidal wave functions with small arguments
, 2002 Power series expansions for the angular spheroidal wave functions of the first kind Smn(c,η), with small arguments c, are derived for general integer values of m and n.
Gerassimos C. Kokkorakis +5 more
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