SOME REMARKS ON THE PERIODIC CONTINUED FRACTION

  • Lee, Yeo-Rin (Department of Mathematics Eduacation Pusan University of Foreign Studies)
  • Received : 2009.01.11
  • Accepted : 2009.02.17
  • Published : 2009.06.30

Abstract

Using the Binet's formula, we show that the quotient related ratio $l_{1(x)}\;\neq\;0$ for the eventually periodic continued fraction x. Using this ratio, we also show that the derivative of the Minkowski question mark function at the simple periodic continued fraction is infinite or 0. In particular, $l_1({[\bar{1}]})$ = 2 log $\gamma$ where $\gamma$ is the golden mean $(1+\sqrt{5})/2$ and the derivative of the Minkowski question mark function at the simple periodic continued fraction $[\bar{1}]$ is infinite.

Keywords

References

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