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THE FIXED POINT FOR A TRANSFORMATION OF HAUSDORFF MOMENT SEQUENCES AND ITERATION OF A RATIONAL FUNCTION

CHRISTIAN BERG and ANTONIO J. DURÁN
Mathematica Scandinavica
Vol. 103, No. 1 (2008), pp. 11-39
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24493599
Page Count: 29
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
THE FIXED POINT FOR A TRANSFORMATION OF HAUSDORFF MOMENT SEQUENCES AND ITERATION OF A RATIONAL FUNCTION
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Abstract

We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: T((an))n = 1/(a0 + ··· + an). We determine the corresponding measure μ, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. The Mellin transform F of μ extends to a meromorphic function in the whole complex plane. It can be characterized in analogy with the Gamma function as the unique log-convex function on ]-1, ∞[ satisfying F(0) = 1 and the functional equation 1/F(s) = 1/F(s + 1) - F(s + 1), s > -1.

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