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Mathematics LibreTexts

3: Questions Concerning Power Series


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  • 3.1: Taylor’s Formula
    As we saw in the previous chapter, representing functions as power series was a fruitful strategy for mathematicans in the eighteenth century (as it still is). Differentiating and integrating power series term by term was relatively easy, seemed to work, and led to many applications. Furthermore, power series representations for all of the elementary functions could be obtained if one was clever enough.
  • 3.2: Series Anomalies
    Eighteenth century mathematicians who ingeniously exploited calculus and series to provide mathematical and physical results which were virtually unobtainable before. Mathematicians were eager to push these techniques as far as they could to obtain their results and they often showed good intuition regarding what was mathematically acceptable and what was not. However, as the envelope was pushed, questions about the validity of the methods surfaced.
  • 3.E: Questions Concerning Power Series (Exercises)


  • Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)