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Appendices

# A1 Taylor Series

## Function of a Single Variable

Taylor series expansion of a function f(x) about the point x = a is the infinite series

 (A1)

In the special case a = 0 the series is also known as the MacLaurin series. It can be shown that Taylor series expansion is unique in the sense that no two functions have identical Taylor series.

A Taylor series is meaningful only if all the derivatives of f(x) exist at x = a and the series converges. In general, convergence occurs only if x is sufficiently close to a; that is, if |x-a| ≤ ε, where ε is called the radius of convergence. In many cases ε is infinite.

Another useful form of a ...

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