The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

• Autores: Christian Berg, Antonio José Durán Guardeño
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 103, Nº 1, 2008, págs. 11-39
• Idioma: inglés
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• Resumen

  • We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences, defined by the formula: T ((an))n = 1/(a0+�E �E �E+an).We determine the corresponding measure�Ê, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. TheMellin transform F of �Ê extends to ameromorphic 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.