Binomial Sums Related to Rational Approximations to ζ(4)

@article{Zudilin2004BinomialSR,
  title={Binomial Sums Related to Rational Approximations to ζ(4)},
  author={V. V. Zudilin},
  journal={Mathematical Notes},
  year={2004},
  volume={75},
  pages={594-597}
}
  • V. V. Zudilin
  • Published 2004
  • Mathematics
  • Mathematical Notes
  • Abstract. For the solution {u n } ∞n=0 to the polynomial recursion (n + 1) 5 u n+1 −3(2n + 1)(3n 2 + 3n + 1)(15n 2 + 15n + 4)u n − 3n 3 (3n − 1)(3n + 1)u n−1 = 0, wheren = 1,2,..., with the initial data u 0 = 1, u 1 = 12, we prove that all u n are integers.The numbers u n , n = 0,1,2,..., are denominators of rational approximations to ζ(4)(see math.NT/0201024). We use Andrews’s generalization of Whipple’s transformationof a terminating 7 F 6 (1)-series and the method from math.NT/0311114… CONTINUE READING
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