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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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