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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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On the Exponential and Trigonometric $$q,\omega $$-Special Functions
2020The 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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Complex Numbers: Complex Exponential and Trigonometric Functions
1980This 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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Defining Exponential and Trigonometric Functions Using Differential Equations
Mathematics Magazine, 2014SummaryThis note addresses the question of how to rigorously define the functions exp(x), sin(x), and cos(x), and develop their properties directly from that definition. We take a differential equations approach, defining each function as the solution of an initial value problem.
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On the exact value of a complete trigonometric sum with an exponential function
Mathematical Notes, 1992Let \(p\) be an odd prime, and \(a\), \(b\), \(q\) integers such that \((a,b,p)=1\) and \((q,p)=1\). Suppose that \(\tau\) is the order of \(q\bmod p\), \(\Delta= \text{ord}_ p (q^ \tau-1)\), \(\alpha\geq\Delta\) is an integer, \(\tau_ \alpha= p^{\alpha-\Delta}\tau\), \(\varepsilon_ 0= q^ \tau\) and \(U_ p\) is the group of the units of the field ...
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Transcendental Functions: Exponential, Logarithmic, Trigonometric
2023Andrei Bourchtein, Ludmila Bourchtein
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Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
Mathematica Slovaca, 2021Imdat İşcan +2 more
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Exponential and Trigonometric Functions
1978Harley Flanders, Justin J. Price
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