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We consider the number $\pi$coth $\pi$ which is transcendental in view of algebraic independence of $\pi$ and $e^{\pi}$ (due to Nesterenko's work in 1996). Studying certain nearly�poised hypergeometric series with complex parameters, which give us linear forms in $\pi$coth $\pi$ and 1 with rational coefficients and applying Zeilberger's algorithm of creative telescoping we obtain a second order difference equation for these forms and their coefficients. As a consequence, we find a new decomposition of $\pi$coth $\pi$ into a continued fraction, which produces a rapidly convergent sequence of rational approximations to this number.
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