Irrationality proof of a q-extension of ζ(2) using little q-Jacobi polynomials
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چکیده
We show how one can use Hermite-Padé approximation and little q-Jacobi polynomials to construct rational approximants for ζq(2). These numbers are qanalogues of the well known ζ(2). Here q = 1 p , with p an integer greater than one. These approximants are good enough to show the irrationality of ζq(2) and they allow us to calculate an upper bound for its measure of irrationality: μ (ζq(2)) ≤ 10π2/(5π2 − 24) ≈ 3.8936. This is sharper than the upper bound given by Zudilin (On the irrationality measure for a q-analogue of ζ(2), Mat. Sb. 193 (2002), no. 8, 49–70).
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تاریخ انتشار 2008