# Boundary Value Problems/Series Solutions

${\displaystyle \sum _{n=0}^{\infty }{\frac {f^{(n)}(a)}{n!}}(x-a)^{n}\,,}$ 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 ${\displaystyle f(x)}$ we write ${\displaystyle f(x)=\sum _{n=0}^{\infty }{\frac {f^{(n)}(a)}{n!}}(x-a)^{n}\,,}$
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