Vol. 56, No. 2, 1975

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The Padé table of functions having a finite number of essential singularities

Albert Edrei

Vol. 56 (1975), No. 2, 429–453
Abstract

Let f(z) be regular at the origin and let it be single-valued and regular except for poles and s + 1 < + essential singularities α012,σ. The α’s may be limit-points of poles and α0 = is permissible. Assume that αk is of finite order λk and let Λ = λk.

The author obtains a convergence theorem for the Padé table of ajzj = f(z). The simplest consequence of his result may be stated as follows: if Λ < 2, the diagonal approximants of the Padé table converge almost everywhere in the plane.

Mathematical Subject Classification
Primary: 30A82
Milestones
Received: 6 November 1973
Published: 1 February 1975
Authors
Albert Edrei