A hypergeometric problem.(English)Zbl 1178.33007

The author poses a problem to prove some identity for hypergeometric-type series which are related to the remainders of rational approximations to $$\zeta(4).$$

MSC:

 33C20 Generalized hypergeometric series, $${}_pF_q$$
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References:

 [1] Zudilin, W., Well-poised hypergeometric service for Diophantine problems of zeta values,in: actes des 12èmes rencontres arithmétiques de caen (June 29-30, 2001), J. théorie nombres Bordeaux, 15, 2, 593-626, (2003) [2] Krattenthaler, C.; Rivoal, T., Hypergéométrie et fonction zêta de Riemann, Mem. amer. math. soc., 186, 875, (2007) · Zbl 1113.11039 [3] Zudilin, W., Binomial sums related to rational approximations to $$\zeta(4)$$, Mat. zametki, 75, 4, 637-640, (2004), (English transl., Math. Notes 75 (4) (2004) 594-597). arXiv:math/0311196 [4] Bailey, W.N., (), 2nd reprinted edition, Stechert-Hafner, New York, London, 1964
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