%0 Journal Article %T Orthogonal polynomials for Minkowski's question mark function %A Zo¨¦ Dresse %A Walter Van Assche %J Mathematics %D 2014 %I arXiv %R 10.1016/j.cam.2014.07.013 %X 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 $(P_n)_{n \in \mathbb{N}}$ 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. %U http://arxiv.org/abs/1403.1374v2