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Type II Hermite–Padé Approximations of Generalized Hypergeometric Series

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Abstract

We shall present short proofs for type II (simultaneous) Hermite–Padé approximations of the generalized hypergeometric and q-hypergeometric series

$$F(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(k)}{\prod _{k=0}^{n-1}Q(k)}t^n,\qquad F_q(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(q^k)}{\prod _{k=0}^{n-1}Q(q^k)}t^n,$$

where P and Q are polynomials. Further, a comparison is made between the remainder series approximations of the exponential series (Prévost and Rivoal) and recent modified approximations of a q-analog of the exponential series.

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  1. Matemaattisten tieteiden laitos, PL 3000, 90014, Oulun Yliopisto, Finland

    Tapani Matala-aho

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  1. Tapani Matala-aho
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Correspondence to Tapani Matala-aho.

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Communicated by Erik Koelink.

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Matala-aho, T. Type II Hermite–Padé Approximations of Generalized Hypergeometric Series. Constr Approx 33, 289–312 (2011). https://doi.org/10.1007/s00365-010-9111-x

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  • DOI: https://doi.org/10.1007/s00365-010-9111-x

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