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Power Series

Power Series. Mika Seppälä. Power Series. Definition. A power series is a series of the type.

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Power Series

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  1. Power Series Mika Seppälä

  2. Power Series Definition A power series is a series of the type Here x is a variable. Substituting a numeric value x=x0 for the variable x one gets a regular series P(x0). If this regular series converges, then we say that the power series P(x) converges at the point x=x0. Example We conclude that the power series P(x) converges for all values of x, -1<x<1, and diverges otherwise. Mika Seppälä: Power Series

  3. Radius of Convergence The limit is the radius of convergence of the power series P(x) provided that the limit exists. The power series P(x) converges for |x|<R and diverges for|x|>R. At the points x=R and x=-R the series may converge or diverge. Definition Mika Seppälä: Power Series

  4. Example Mika Seppälä: Power Series

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