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% exponentialreihe.tex -- slide template
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% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
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\frametitle{Exponentialreihe}
\begin{align*}
h(s) &= \exp(tA_0 + sB) = \sum_{k=0}^\infty \frac{1}{k!} (tA_0 + sB)^k
\\
&=
I + (tA_0 + sB) + \frac{1}{2!}(t^2A_0^2 + ts(A_0B + BA_0) + s^2B^2)
+ \frac{1}{3!}(t^3A_0^3 + t^2s(A_0^2B + A_0BA_0 + BA_0^2) + \dots)
+ \dots
\\
\frac{dg(s)}{ds}
&=
B + \frac1{2!}t(A_0B+BA_0) + \frac{1}{3!}t^2(A_0^2B+A_0BA_0+BA_0^2) + \dots
\end{align*}
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