What is the finite expansion of a function means ?

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Za Kh
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i know the rules of finite expansion but i just want to know why do we need it and what does it mean ?
 
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The phrase "finite expansion" isn't specific. Can you give an example?
 
If you're referring to the Taylor expansion, this site provides several good reasons and examples. The reasons they list are approximations of all sorts, series solutions of differential equations, and limiting values.