A Remark on the Arcsine Distribution and the Hilbert transform
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DOI: 10.1007/s00041-019-09678-w
Abstract: It is known that if $$(p_n)_{n \in \mathbb {N}}$$(pn)n∈N is a sequence of orthogonal polynomials in $$L^2([-1,1], w(x)dx)$$L2([-1,1],w(x)dx), then the roots are distributed according to an arcsine distribution $$\pi ^{-1} (1-x^2)^{-1}dx$$π-1(1-x2)-1dx for a wide variety… read more here.
Keywords: arcsine distribution; remark arcsine; hilbert transform;