Difference between revisions of "Schröder equation"
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For a given function $f$ and constant $c$ find a function $\sigma$ such that | For a given function $f$ and constant $c$ find a function $\sigma$ such that | ||
$$\sigma(f(x))=c \sigma(x).$$ | $$\sigma(f(x))=c \sigma(x).$$ | ||
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| + | The Schröder equation can be transformed into the form of an [[Abel equation]]: | ||
| + | $$\log_c\!\Big(\sigma\big(f(x)\big)\Big)=1+\log_c(\sigma(x))$$ | ||
Latest revision as of 15:07, 15 December 2012
For a given function $f$ and constant $c$ find a function $\sigma$ such that $$\sigma(f(x))=c \sigma(x).$$
The Schröder equation can be transformed into the form of an Abel equation: $$\log_c\!\Big(\sigma\big(f(x)\big)\Big)=1+\log_c(\sigma(x))$$