%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