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Some convergence results in simultaneous rational approximation to the set of hypergeometric functions {1F1(1;ci;z)} ni=1

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Padé Approximation and its Applications Bad Honnef 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1071))

Abstract

Using explicit formulae for the denominators PO(z) of degree σ-ρO and the remainders PO(z)1F1(1;ci;z) − Pi(z) (power series starting with za+1 where a ≥ σ = ρO + ρ1 + ... + ρn and the Pi are polynomials of degree σ-ρi (i = 1, 2,...,n)) convergence of the simultaneous Padé approximants Pi(z)/PO(z) to 1F1(1;ci;z) (i = 1,2,...,n) under the conditions ρO ≥ ρi-1 (i = 1,2,...,n) and σ→∞ is proved.

Furthermore it is shown that the numerator- and denominator-polynomials converge separately in case ρi/ρO → ωi for ρO → ∞ (i = 1,2,...,n).

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Authors and Affiliations

  1. Department of Mathematics, University of Amsterdam, Box 20239, 1000 HE, Amsterdam, The Netherlands

    Marcel G. de Bruin

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  1. Marcel G. de Bruin
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Helmut Werner Hans Josef Bünger

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© 1984 Springer-Verlag

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de Bruin, M.G. (1984). Some convergence results in simultaneous rational approximation to the set of hypergeometric functions {1F1(1;ci;z)} ni=1 . In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099607

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  • DOI: https://doi.org/10.1007/BFb0099607

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