Iterated function: Difference between revisions

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Chebyshev self-composition results in an exponential increase in the index, not a linear one.
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| <math>T_m (x)=\cos (m \arccos x)</math> ([[Chebyshev polynomials#Trigonometric definition|Chebyshev polynomial]] for integer ''m'')
| <math>T_{mnm^n}=\cos(m^n \arccos x)</math>
|}
Note: these two special cases of {{math|''ax''<sup>2</sup> + ''bx'' + ''c''}} are the only cases that have a closed-form solution. Choosing ''b'' = 2 = –''a'' and ''b'' = 4 = –''a'', respectively, further reduces them to the nonchaotic and chaotic logistic cases discussed prior to the table.