Let f , g : R → R {\displaystyle {}f,g\colon \mathbb {R} \rightarrow \mathbb {R} } be polynomials of degree n {\displaystyle {}n} , let a 1 , … , a k ∈ R {\displaystyle {}a_{1},\ldots ,a_{k}\in \mathbb {R} } be points and n 1 , … , n k ≥ 1 {\displaystyle {}n_{1},\ldots ,n_{k}\geq 1} natural numbers fulfilling
Suppose that the derivatives of f {\displaystyle {}f} and g {\displaystyle {}g} coincide in den points a j {\displaystyle {}a_{j}} up to the ( n j − 1 ) {\displaystyle {}{\left(n_{j}-1\right)}} -th derivative. Show
be polynomials of degree 
, let
be points and
natural numbers fulfilling
and 
coincide in den points 
up to the 
-th derivative. Show
