Orthogonal polynomials for Minkowski's question mark function

Hermann Minkowski introduced a function in 1904 which maps quadratic irrational numbers to rational numbers and this function is now known as Minkowski's question mark function since Minkowski used the notation ? ( x ) . This function is a distribution function on 0 , 1 which defines a singular continuous measure with support 0 , 1 . Our interest is in the (monic) orthogonal polynomials ( P n ) n � N for the Minkowski measure and in particular in the behavior of the recurrence coefficients of the three term recurrence relation. We will give some numerical experiments using the discretized Stieltjes-Gautschi method with a discrete measure supported on the Minkowski sequence. We also explain how one can compute the moments of the Minkowski measure and compute the recurrence coefficients using the Chebyshev algorithm.

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