Quadratic Irrationals, Generating Functions, and L\'evy Constants
classification
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quadraticfunctiongeneratingirrationalrationalapproximantsbestcoefficients
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We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\'evy constant of any quadratic irrational explicitly in terms of a finite number of its convergents.
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