Results 1 to 10 of about 12,886 (197)
Axioms, 2022 In this paper, the Fourier series expansion of Tangent polynomials of higher order is derived using the Cauchy residue theorem. Moreover, some variations of higher-order Tangent polynomials are defined by mixing the concept of Tangent polynomials with ...
Cristina Bordaje Corcino +1 more
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A Novel Approach in Solving Improper Integrals
Axioms, 2022 To resolve several challenging applications in many scientific domains, general formulas of improper integrals are provided and established for use in this article.
Mohammad Abu-Ghuwaleh +2 more
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General Master Theorems of Integrals with Applications
Mathematics, 2022 Many formulas of improper integrals are shown every day and need to be solved in different areas of science and engineering. Some of them can be solved, and others require approximate solutions or computer software.
Mohammad Abu-Ghuwaleh +2 more
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New Theorems in Solving Families of Improper Integrals
Axioms, 2022 Many improper integrals appear in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik. It is a challenge for some researchers to determine the method in which these integrations are formed or solved. In this article, we present some new
Mohammad Abu Ghuwaleh +2 more
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Finding the Zeros of a High-Degree Polynomial Sequence
Journal of Optimization, Differential Equations and Their Applications, 2021 A 1-parameter initial-boundary value problem for a linear spatially 1-dimensional homogeneous degenerate wave equation, posed in a space-time rectangle, in case of strong degeneracy, was reduced to a linear integro-differential equation of convolution ...
Vladimir L. Borsch, Peter I. Kogut
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Relationship Between Cauchy Integral Theorem and Residue Theorems
Highlights in Science, Engineering and Technology, 2023 Cauchy integral theorem belongs to an extremely important part of complex functions, which is a fundamental bridge, and people can derive Cauchy integral theorem from the residue theorem. Cauchy's integral theorem is generally applied in many higher mathematics, is an important theorem concerning path integrals of fully pure functions.
Jiaming Guo, Biran Song
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Mathematical and Computational Applications, 2022 In this paper, we focus on investigating the performance of the mathematical software program Maple and the programming language MATLAB when using these respective platforms to compute the method of steps (MoS) and the Laplace transform (LT) solutions ...
Michelle Sherman +2 more
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A Formal Proof of Cauchy’s Residue Theorem [PDF]
, 2016 We present a formalization of Cauchy’s residue theorem and two of its corollaries: the argument principle and Rouché’s theorem. These results have applications to verify algorithms in computer algebra and demonstrate Isabelle/HOL’s complex analysis library.
Li, W, Paulson, LC
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Cauchy Theorem and Cauchy Residue Theorem
Highlights in Science, Engineering and Technology, 2023 Cauchy theorem is widely used in solving analytic function problems in complex variables. It is an important theorem on path integrals of holomorphic functions in the complex plane. In this paper, the main work is about the application of the Cauchy theorem on the integrals which have singularities.
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Cauchy Residue Theorem and K-residue Theorem
Highlights in Science, Engineering and Technology, 2023 Due to negative numbers do not have square roots, scientists introduced complex numbers, which are more abstract compared with real numbers. Residue Theorem has a very significant status in complex analysis – it can be used to simplify difficult integrals. In this article, Cauchy’s Residue Theorem is first introduced with definition and proof. Then the
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