${\displaystyle {}a,b}$

${\displaystyle {}K}$

${\displaystyle {}(a+b)^{n}=\sum _{i=0}^{n}{\binom {n}{i}}a^{i}b^{n-i}\,.}$

${\displaystyle {}z}$

${\displaystyle {}{|z|}<1}$

${\displaystyle {}\sum _{k=0}^{\infty }z^{k}}$

${\displaystyle {}\sum _{k=0}^{\infty }z^{k}={\frac {1}{1-z}}\,.}$

${\displaystyle {}f=\sum _{n=0}^{\infty }a_{n}z^{n}}$

${\displaystyle {}g=\sum _{n=0}^{\infty }b_{n}z^{n}}$

${\displaystyle {}\epsilon >0}$

${\displaystyle f,g\colon U{\left(0,\epsilon \right)}\longrightarrow {\mathbb {K} }}$

${\displaystyle {}a_{n}=b_{n}}$

${\displaystyle {}n\in \mathbb {N} }$

${\displaystyle {}I}$

${\displaystyle f\colon I\longrightarrow \mathbb {R} }$

eine stetige Funktion. Es sei

${\displaystyle g\colon [a,b]\longrightarrow I}$

stetig differenzierbar. Dann gilt

${\displaystyle {}\int _{a}^{b}f(g(t))g'(t)\,dt=\int _{g(a)}^{g(b)}f(s)\,ds\,.}$