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.

$\sum _{n=0}^{\mathrm{\infty }}\frac{f^{(n)}(a)}{n!}(x-a{)}^n,$ 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 − a)⁰ and 0! are both defined to be 1.

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

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