Geodesic
Rhin Integrals
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 226-239

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a generalization of the integrals examined by G. Rhin, in the form of multiple integrals. These integrals yield rational approximations to the values of the Riemann zeta function. In a particular case, we obtain Apéry approximations used to prove the irrationality of the number $\zeta(3)$.
Keywords: Rhin integral, Riemann zeta function, multiple integral, Apéry approximation, Beukers integral, hypergeometric function.
Mots-clés : polylogarithm 
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     author = {S. A. Zlobin},
     title = {Rhin {Integrals}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {226--239},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a6/}
}
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S. A. Zlobin. Rhin Integrals. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 226-239. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a6/