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November 2019 Power Series Extensions of Certain Functions of a Real Variable
Scott H. Demsky, Alex Opritsa
Missouri J. Math. Sci. 31(2): 107-112 (November 2019). DOI: 10.35834/2019/3102107

Abstract

The domain of the function $ f(x)=\cos \sqrt{x} $ is the set of all nonnegative real numbers. In this article, we will show how to use power series to extend this function to an analytic function defined on the entire real line. We will then show how this analytic extension of $ f(x) $ makes it easier and quicker for calculus students to compute derivatives of $ f(x) $ at the origin. We will moreover describe the process of extending the domain of any function of the form $ g(\sqrt{x}) $ for a given even analytic function $ g(x) $.

Citation

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Scott H. Demsky. Alex Opritsa. "Power Series Extensions of Certain Functions of a Real Variable." Missouri J. Math. Sci. 31 (2) 107 - 112, November 2019. https://doi.org/10.35834/2019/3102107

Information

Published: November 2019
First available in Project Euclid: 16 November 2019

zbMATH: 07276117
MathSciNet: MR4032187
Digital Object Identifier: 10.35834/2019/3102107

Subjects:
Primary: 26A06
Secondary: 40A05

Rights: Copyright © 2019 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.31 • No. 2 • November 2019
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