Boundary Value Problems/Series Solutions

In your Calculus course you were introduced to Power Series and the representation of certain types of functions using Taylor series.

$$\sum_{n=0}^{\infin} \frac{f^{(n)}(a)}{n!} (x-a)^{n}\,,$$ where n! is the factorial of n and f(n)(a) denotes the nth derivative of f evaluated at the point a; the zeroth derivative of f is defined to be f itself and (x &minus; a)0 and 0! are both defined to be 1.

If the Taylor series converges to $$ f(x) $$ we write $$ f(x)=\sum_{n=0}^{\infin} \frac{f^{(n)}(a)}{n!} (x-a)^{n}\,,$$

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