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- European Southern ObservatoryCL46 papers
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7 papers · 1 filter
Fibonacci numbers, Euler's 2-periodic continued fractions and moment sequences
Christian Berg, Antonio J. Durán
We prove that certain sequences of finite continued fractions associated with a 2-periodic continued fraction with period a,b>0 are moment sequences of discrete signed measures sup…
Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
Stamatis Koumandos, Henrik L. Pedersen
We introduce completely monotonic functions of order and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma…
Bounds on Tur{á}n determinants
Christian Berg, Ryszard Szwarc
Let μdenote a symmetric probability measure on [-1,1] and let (p_n) be the corresponding orthogonal polynomials normalized such that p_n(1)=1. We prove that the normalized Tur{á}n…
Quantum Hilbert matrices and orthogonal polynomials
Jorgen Ellegaard Andersen, Christian Berg
Using the notion of quantum integers associated with a complex number , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding…
On powers of Stieltjes moment sequences, II
Christian Berg
We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of…
Integral representation of some functions related to the Gamma function
Christian Berg
We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.