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Key words: cumulative Bernoulli trials; multivariate Markov chains; 9 − j symbols; transition kernel; Askey–Wilson polynomials; eigenvalue problem; trinomial distribution;
Key words: elliptic Frobenius determinant; QD -algorithm; orthogonal and biorthogonal polynomials on the unit circle; dense point spectrum; elliptic hypergeometric
[3] Cooper R.D., Hoare M.R., Rahman M., Stochastic processes and special functions: on the probabilistic origin of some positive kernels associated with classical
We prove that one characterization for the classical orthogonal polynomials sequences (Hermite, Laguerre, Jacobi and Bessel) cannot be extended to the semi-classical ones..
Remark For our special choice of the selection matrix (additive selection) the last term in (1.13) can be simplified and this will be used occasionally so we write this out
Nevertheless [1] indeed showed that the 1-potential density of an isotropic stable additive process is comparable to the Riesz kernel at 0, and therefore the 1-potential density
Representations of quantum groups and realizations of q - oscillators are closely related to basic hypergeometric functions and q -orthogonal polynomials.. Instead of Jacobi,
We study multivariable Christoffel–Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation func- tions for
