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<math>f</math> is around {{pi}} the contraction mapping from the obvious reasons because its derivative in {{pi}} vanishes therefore {{pi}} can be obtained from the infinite superposition for example for the argument value 3:
<math>\pi=f(f(f(...f(3)...))))</math>
Already the triple superposition of this function at <math>3</math> gives {{pi}} with accuracy to 33 digits:
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