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m link [pP]ower series |
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:<math>z = f(w)</math>
where {{mvar|f}} is analytic at a point {{mvar|a}} and <math>f'(a)\neq 0.</math> Then it is possible to ''invert'' or ''solve'' the equation for {{mvar|w}}, expressing it in the form <math>w=g(z)</math> given by a [[power series]]<ref>{{cite book |editor=M. Abramowitz |editor2=I. A. Stegun |title=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables |chapter=3.6.6. Lagrange's Expansion |place=New York |publisher=Dover |page=14 |year=1972 |url=http://people.math.sfu.ca/~cbm/aands/page_14.htm}}</ref>
:<math> g(z) = a + \sum_{n=1}^{\infty} g_n \frac{(z - f(a))^n}{n!}, </math>
where
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