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Home Infinite Series Derivatives and Integrals of Power Series Examples Example 1: Derivative and Integral | |
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Example 1: Derivative and Integral
Differentiate and integrate the power series , and find the radii of convergence. By the Ratio Test this power series has radius of convergence r = 1, for Derivative: Integral: For convenience we rewrote the derivative as a power series in xm where m = n - 1, and the integral as a power series in xm where m = n + 1. Both the derivative and integral also have radius of convergence r = 1.
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Home Infinite Series Derivatives and Integrals of Power Series Examples Example 1: Derivative and Integral |