Abstract
Many functions arising in basic applications are not elementary; however, many of them can be well approximated by a polynomial in x. Thus ∫sin x/x dx cannot be expressed as a simple elementary function but can be approximated to any desired accuracy by a polynomial in x, the approximation improving with increase in the degree of the polynomial used. In a certain sense, many of the functions arising in basic applications can be represented exactly b a polynomial of infinite degree, called an infinite power series. This chapter aims to give meaning to this last sentence, and to provide specific techniques for representing functions by infinite power series. The chapter explains the integral test for convergence.
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