Transcription of INFINITE SERIES - Elsevier.com
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INFINITE SERIES - Elsevier.com
Chapter 1 INFINITE SERIESChap1 This on-line chapter contains the material on INFINITE SERIES , extracted from the printedversion of the Seventh Edition and presented in much the same organization in whichit appeared in the Sixth Edition. It is collected here for the convenience of instructorswho wish to use it as introductory material in place of that in the printed book. It hasbeen lightly edited to remove detailed discussions involving complex variable theorythat would not be appropriate until later in a course of instruction. For AdditionalReadings, see the printed INTRODUCTION TO INFINITE the most widely used technique in the physicist s toolbox is the use ofinfiniteseries( sums consisting formally of an INFINITE number of terms) to representfunctions, to bring them to forms facilitating further analysis, or even as a preludeto numerical evaluation.
6 CHAPTER 1. INFINITE SERIES To free the integral test from the quite restrictive requirement that the interpo-lating function f(x) be positive and monotonic, we shall show that for any function f(x) with a continuous derivative, the inflnite series is exactly represented as a sum of two integrals: XN2 n=N1+1 f(n) = Z N 2 N1 f(x)dx+ Z N 2 N1 N1
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