SOME REMARKS ON THE PERIODIC CONTINUED FRACTION

Abstract

Using the Binet's formula, we show that the quotient related ratio l1(x) 6= 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, l1([1]) = 2 log γ where γ 5)/2 and the derivative of the Minkowski is the golden mean (1 + question mark function at the simple periodic continued fraction [1] is infinite.

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