The symmetric strong moment problem
The authors study continued fractions corresponding to the two series \[ \begin{aligned} L_\infty(z) &=\mu_0z^{-1}+ \mu_1z^{-2}+\mu_2z^{-3}+\cdots\\ L_0(z) &=-\mu_{-1}- \mu_{-2}z-\mu_{-3}z^2-\cdots\end{aligned} \] at \(z=\infty\) and \(z=0\) respectively, in the special case where \(\mu_{-n}=\mu_n\) for all \(n\). The particular case where \(\{\mu_n\}\) is the solution of a strong Stieltjes moment problem is of special interest. Two sequences of corresponding orthogonal polynomials are derived and the connection between them established. Finally, the results are applied to the log-normal distribution.
scientific article; zbMATH DE number 908378
scientific article