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Responding to Matt F.'s comment.
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Joseph O'Rourke
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Not an answer, just a plot of $F_n(x)$ for $n=2,\ldots,10$:


          [![Fn(x)][1]][1]
          [![Fn(x)2][2]][2]

Not an answer, just a plot of $F_n(x)$ for $n=2,\ldots,10$:


          [![Fn(x)][1]][1]

Not an answer, just a plot of $F_n(x)$ for $n=2,\ldots,10$:


          [![Fn(x)][1]][1]
          [![Fn(x)2][2]][2]
Source Link
Joseph O'Rourke
  • 150.8k
  • 36
  • 358
  • 958

Not an answer, just a plot of $F_n(x)$ for $n=2,\ldots,10$:


          [![Fn(x)][1]][1]