The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
نویسنده
چکیده
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. 2000 Mathematics Subject Classification: primary 44A60; secondary 30D05.
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تاریخ انتشار 2006