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Paper   IPM / M / 8874
School of Mathematics
  Title:   An Apery-like continued fraction for πcothπ
1.  Kh. Hessami Pilehrood
2.  T. Hessami Pilehrood
  Status:   To Appear
  Journal: J. Difference Equ. Appl.
  Supported by:  IPM
We consider the number πcoth π which is transcendental in view of algebraic independence of π and eπ (due to Nesterenko's work in 1996). Studying certain nearly�poised hypergeometric series with complex parameters, which give us linear forms in πcoth π 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 πcoth π into a continued fraction, which produces a rapidly convergent sequence of rational approximations to this number.

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