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November 2021 Taylor Series for $\frac{1}{1+x^2}$ at $x=a$
Scott H. Demsky, Sanford Geraci
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Missouri J. Math. Sci. 33(2): 158-162 (November 2021). DOI: 10.35834/2021/3302158

Abstract

We determine a formula for all coefficients of the Taylor series for the function $ \frac{1}{1+x^2} $ centered at $ x=a $ for any real number $ a $ along with the radius of convergence of the series. We utilize complex numbers to extend a standard calculus technique involving geometric series, but we write the coefficients using real numbers only.

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Scott H. Demsky. Sanford Geraci. "Taylor Series for $\frac{1}{1+x^2}$ at $x=a$." Missouri J. Math. Sci. 33 (2) 158 - 162, November 2021. https://doi.org/10.35834/2021/3302158

Information

Published: November 2021
First available in Project Euclid: 30 November 2021

Digital Object Identifier: 10.35834/2021/3302158

Subjects:
Primary: 41A58

Keywords: calculus , complex variables , geometric series , Radius of convergence , Taylor series

Rights: Copyright © 2021 University of Central Missouri, School of Computer Science and Mathematics

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Vol.33 • No. 2 • November 2021
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