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Convergence and Analytic Continuation for a Class of Regular C-Fractions

Published online by Cambridge University Press:  20 November 2018

D. Masson
D. Masson*
Affiliation:
University of TorontoToronto, Ontario, Canada
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Abstract

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Regular C-fractions f(α) = 1 + a1α/1 + a2α/1 + . .. with an = an2 + bn + c + Vn, |Vn| sufficiently small are examined. In the case Vn = 0, exact expressions are obtained which reveal a two sheeted Riemann structure for f(α). If Vn ≠ 0 analytic properties are obtained by means of perturbation theory applied to the associated difference equation. A conjecture that f(α) is the ratio of two entire functions of for an even larger class of C-fractions is proved for the case .

Keywords

30B7039A1040A1533A30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 411 - 421
Copyright
Copyright © Canadian Mathematical Society 1985

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