Provided certain conditions are met, we can expand the function f(x) in an infinite power series about
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Differentiate (4.84) m times, and then set x = a to show that cn = f(n)(a)/n!, thus giving the familiar Taylor series:
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f(x) = Σ (xa)" (4.84) n=0 f(x)y(n)(a) n=0 n! (4.85)
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Taking d dx m of 484 gives f m x n0 c n nn 1 n 2 n m 1 x a nm The factors n n 1 make the terms wit...View the full answer
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