Notes for AKT-090922/0:08:20

Theorem (from last time) If we expand:

[math]\displaystyle{ J(K)(e^x)=\sum{J_n(K)x^n} }[/math]

then [math]\displaystyle{ J_n }[/math] is an invariant of type [math]\displaystyle{ n }[/math].

In fact, this holds if we substitute [math]\displaystyle{ e^x }[/math] by any power series that starts with [math]\displaystyle{ 1+x }[/math] (e.g. [math]\displaystyle{ 1+x }[/math], [math]\displaystyle{ 1+sinx }[/math]).