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Exponential-Trigonometric Optimization Algorithm for Solving Complicated Engineering Problems
Computer Methods in Applied Mechanics and EngineeringThis article presents an innovative optimization algorithm called the Exponential-Trigonometric Optimization (ETO) algorithm, which is based on a sophisticated combination of exponential and trigonometric functions.
Le Thanh Cuong +2 more
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On fractional derivatives of trigonometric functions and exponential functions
Chaos: An Interdisciplinary Journal of Nonlinear ScienceIn some places, fractional derivative is abbreviated as Dα, dαdtα(ordαdxα), where α is positive but not an integer. The “formulas” dαsintdtα=sin(t+πα2), dαcostdtα=cos(t+πα2), and dαeλtdtα=λαeλt are sometimes used. However, they generally hold for α∈Z+={0,1,2,…}.
Changpin Li, Jianhua Tang
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A NOTE ON TWO RESULTS ASSOCIATED WITH EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS
Far East Journal of Mathematical Sciences (FJMS), 2016Summary: The objective of this note is to show how we can establish Taylor-Maclaurin series expansions of products of exponential and trigonometric functions in an elementary way.
Sukanya, M. +2 more
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Sharp Exponential Approximate Inequalities for Trigonometric Functions
Results in Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized Exponential and Trigonometric Functions
1993One of the most classical papers written on generalized Fibonacci numbers is that of A. F. Horadam, [8]. In that paper, one will find several of the following properties needed in order to obtain the results found in this article. We start with a special case of the basic definition found in [8].
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On An Interpolation of a Function by Exponential-Trigonometric Natural Splines
UZBEK MATHEMATICAL JOURNALne of the challenges in approximation is the interpolation problem. Splines are often used for function approximation. The theory of splines includes both algebraic and variational approaches. In both cases, the existence, uniqueness, and convergence of splines, along with algorithms for their construction, are studied based on their inherent ...
Shadimetov, Kholmat M., Boltaev, Aziz K.
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Basic Exponential and Trigonometric Functions
2003In this chapter we shall introduce the basic exponential and basic trigonometric functions as solutions of a difference analog of the equation for harmonic motion on a q-quadratic grid. Some of their elementary properties will be derived in order to form the basis for developing the theory of basic Fourier series and study some of their applications in
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Real Exponential, Logarithmic, and Trigonometric Functions for Physicists
2022Real Exponential, Logarithmic, and Trigonometric Functions for Physicists builds on the author's previous books focused on mathematics for scientists. This new work presents a rigorous study of the underlying mathematical functions used in physics and provides its readers a deeper understanding for those studying and practicing the physical sciences.
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Using Differentials to Differentiate Trigonometric and Exponential Functions
The College Mathematics Journal, 2013Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential eq...
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Powers, Exponentials, Logarithms, Trigonometric Functions
2004The general theorems of Chapters II and III have allowed us, in passing, to establish most of the principal properties of the elementary functions which crop up everywhere in analysis. In this chapter we shall go over it all systematically. One can do this in various ways, each as instructive as the other.
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