Results 161 to 170 of about 37,190 (197)

Basic Exponential and Trigonometric Functions

2003
In 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

2022
Real 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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Generalized Exponential and Trigonometric Functions

1993
One 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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Using Differentials to Differentiate Trigonometric and Exponential Functions

The College Mathematics Journal, 2013
Starting 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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On fractional derivatives of trigonometric functions and exponential functions

Chaos: An Interdisciplinary Journal of Nonlinear Science
In some places, fractional derivative is abbreviated as Dα, dαdtα(ordαdxα), where α is positive but not an integer. The “formulas” dαsin⁡tdtα=sin⁡(t+πα2), dαcos⁡tdtα=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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Complex Numbers: Complex Exponential and Trigonometric Functions

1980
This chapter begins by enlarging the basic number system from the set R of real numbers to the set C of complex numbers. It is then first of all necessary to reconsider the substance of Chapters VII – XI for the case in which real-valued sequences and functions are replaced by complex-valued ones.
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On the Exponential and Trigonometric $$q,\omega $$-Special Functions

2020
The purpose of this article is to continue the study of \(q,\omega \)-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al. By introducing the new variable \(\omega \), we develop a quite similar calculus consisting of two dual exponential, hyperbolic and trigonometric functions.
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Exponential and trigonometric functions

2021
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Exponential and Trigonometric Functions

1978
Harley Flanders, Justin J. Price
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Trigonometric and exponential functions

2013
K.A. Stroud, Dexter Booth
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