The Journal of the Indian Mathematical Society

N. P. Callas ¹, W. J. Thron ²

Affiliations
1 Department of Mathematics, U.S. Air Force Academy, Colorado 80840, US
2 University of Colorado, Colorado, US

Abstract

These are the so-called C-fractions or corresponding type continued fractions. Leighton and Scott proved that every power series admits an expansion into a continued fraction of the form (1.1).

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W. J. Thron ¹

Affiliations
1 University of Colorado, Boulder, Colorado, US

Abstract

Recently Piranian and Thron [3] gave a classification of the convergence behavior of sequences of linear fractional transformations. They were interested in part in providing tools which might be helpful in deriving results for continued fractions. No such applications have as yet been forthcoming. In this article we consider the classification problem for a more restricted set of sequences, namely those that map the unit circular disk into itself.

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V. F. Cowling ¹, W. J. Thron ²

Affiliations
1 University of Kentucky, US
2 University of Colorado, US

Abstract

In a recent paper [1] by the present authors concerned with zero-free regions of polynomials

P(z) = a₀ + a₁Z^λ1 + … + a_nZ^λn         (1.1)

where all a_q are assumed to be different from zero, and where the λ_k are positive integers satisfying the relation λ₁ < λ₂ < … < λ_n, the following theorem was proved.

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