Iteration of the rational function z-1/z and a Hausdorff moment sequence

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dc.creatorBerg, Christian
dc.creatorDurán, Antonio J.
dc.date2008-02-07
dc.date.accessioned2026-07-07T09:19:15Z
dc.date.available2026-07-07T09:19:15Z
dc.descriptionIn a previous paper we considered a positive function f, uniquely determined for s>0 by the requirements f(1)=1, log(1/f) is convex and the functional equation f(s)=psi(f(s+1)) with psi(s)=s-1/s. We prove that the meromorphic extension of f to the whole complex plane is given by the formula f(z)=lim_{n\to\infty}psi^{\circ n}(lambda_n(lambda_{n+1}/lambda_n)^z), where the numbers lambda_n are defined by lambda_0=0 and the recursion lambda_{n+1}=(1/2)(lambda_n+sqrt{lambda_n^2+4}). The numbers m_n=1/lambda_{n+1} form a Hausdorff moment sequence of a probability measure μsuch that \int t^{z-1}dμ(t)=1/f(z)
dc.identifierhttps://arxiv.org/abs/0802.0947
dc.identifierhttp://arxiv.org/abs/0802.0947
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154321
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subject30D05, 44A60
dc.titleIteration of the rational function z-1/z and a Hausdorff moment sequence
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