A note on Lagrange interpolation for |x|λ at equidistant nodes

In this note, we discuss the exceptional set E subset of or equal to [-1,1] of points x(0) satisfying the inequality lim(n-->infinity)inf n(-1) log\\x\(lambda)-L-n(f(lambda), x(0))\ <(1)/(2) [(1+x(0))log(1-x(0))+(1-x(0))log(1-x(0))], where lambda > 0, lambda not equal 2, 4,... and L-n(f(lambda),.) is the Lagrange interpolation polynomial of degree at most n to f(lambda)(x) := \x\(lambda) on the interval [-1, 1] associated with the equidistant nodes. It is known that E has Lebesgue measure zero. Here we show that E contains infinite families of rational and irrational numbers.