The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
DOI:
https://doi.org/10.7146/math.scand.a-15066Abstract
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.Downloads
Published
2008-09-01
How to Cite
Berg, C., & Durán, A. j. (2008). The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function. MATHEMATICA SCANDINAVICA, 103(1), 11–39. https://doi.org/10.7146/math.scand.a-15066
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