On the asymptotic behaviour of the quantiles in the gamma distribution

The asymptotic behaviour of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behaviour at infinity are given.Comment: 16 pages. Revised version due to overlap with reference number [4

Filled Julia Sets of Chebyshev Polynomials

We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K⊂ C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev polynomials of K converges weak* to the equilibrium measure on K

Julia Sets of Orthogonal Polynomials

For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {P n } to properties of the support. More precisely we relate the Julia set of P n to the outer boundary of the support, the filled Julia set to the polynomial convex hull K of the support, and the Green’s function associated with P n to the Green’s function for the complement of K

Logarithmic order and type of indeterminate moment problems II

AbstractWe show that there exist indeterminate Stieltjes moment problems with prescribed common logarithmic order and type

Canonical products of small order and related pick functions

AbstractWe show that various functions related to the logarithms of the canonical products Pρ(z)=∏n=1∞(1+z/nρ), ρ>1 and Q(z)=∏n=0∞(1+zqn), q∈(0,1) are Pick functions. As a consequence we find an integral expansion of a function involving the logarithm of Jacksons q-gamma function