]> Definition
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## Definition

A series expansion of a function about an argument $x 0$ is an expression of the form

$A + B ( x − x 0 ) + C ( x − x 0 ) 2 + D ( x − x 0 ) 3 + ⋯$

that can go on forever. These are amazingly useful.

The condition that $exp ⁡ x$ is its own derivative gives relationships between the coefficients, $A , B , C , …$ that allow you to deduce what they all are quickly, given $A$ .

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