Hermite–Padé approximants of generalized hypergeometric functions

Yu. V. Nesterenko

Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 189-219

Résumé

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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