Orthogonal polynomials associated with weighting function w(x) | = | π^(-1/2) k exp(-k^2 ln^2 x) | = | π^(-1/2) k x^(-k^2 ln x) for x element (0, ∞) and k>0. Defining q = exp[-(2k^2)^(-1)], then p_0(x) | = | q^(1/4) p_n(x) | = | ((-1)^n q^(n/2 + 1/4))/sqrt((q;q)_n) sum_(ν = 0)^n[n ν] q^(ν^2) (-sqrt(q)x)^ν, where (q;a)_n is a q-Pochhammer symbol and [n ν] is a q-binomial coefficient.
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