Geodesic
Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions
Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 822-835

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We consider a new approach to estimating the irrationality measure of numbers that are values of the Gauss hypergeometric function. Some of the previous results are improved, in particular, those concerning irrationalities of the form $\sqrt{k}\ln((\sqrt{k}+1)/(\sqrt{k}-1))$ with $k\in\mathbb N$.
Keywords: Gauss hypergeometric function, irrationality measure, Laplace method
Mots-clés : rational fraction, Laurent series. 
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     author = {M. G. Bashmakova},
     title = {Approximation of {Values} of the {Gauss} {Hypergeometric} {Function} by {Rational} {Fractions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {822--835},
     publisher = {mathdoc},
     volume = {88},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a2/}
}
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M. G. Bashmakova. Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions. Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 822-835. http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a2/