Geodesic
Hermite--Pad\'e approximants of generalized hypergeometric functions
Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 189-219

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Explicit constructions of functional approximants of the first and second kind are proposed for some collections of generalized hypergeometric functions. Formulas are proved that express the remainders of the approximants and the approximating polynomials themselves in terms of generalized hypergeometric functions with shifted parameters. Expansions in multidimensional continued fractions of the collections of functions considered are found. All this generalizes classical results related to the Gauss hypergeometric function. 
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     author = {Yu. V. Nesterenko},
     title = {Hermite--Pad\'e approximants of generalized hypergeometric functions},
     journal = {Sbornik. Mathematics},
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     number = {1},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_83_1_a9/}
}
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Yu. V. Nesterenko. Hermite--Pad\'e approximants of generalized hypergeometric functions. Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 189-219. http://geodesic.mathdoc.fr/item/SM_1995_83_1_a9/