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differentiable_function [2016/01/23 19:06]
nikolaj
differentiable_function [2016/01/23 19:07] (current)
nikolaj
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 === Theorems === === Theorems ===
-Let $f(0)=0\neq f'​(0)$,​ then+Let  
 + 
 +$f(0)=0\neq f'​(0)$, ​ 
 + 
 +then
  
 $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$ $\dfrac{ f(y\ f^{-1}(x)) }{y} =x+(y-1)\cdot\dfrac{f''​(0)}{f'​(0)^2}\cdot\dfrac{1}{2}x^2+{\mathcal O}(x^3)$
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