The algebraic independence of Weierstrass functions and some related numbers
The analytic continuation and the order estimate of multiple Dirichlet series
Multiple Dirichlet series of several complex variables are considered. Using the Mellin-Barnes integral formula, we prove the analytic continuation and an upper bound estimate.
The asymptotics of interlacing sequences and the growth of continual Young diagrams
The Bergman kernel: Explicit formulas, deflation, Lu Qi-Keng problem and Jacobi polynomials
We investigate the Bergman kernel function for the intersection of two complex ellipsoids We also compute the kernel function for and show deflation type identity between these two domains. Moreover in the case that we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem.
The beta Gumbel distribution.
The Boubaker polynomials expansion scheme BPES for solving a standard boundary value problem.
The Capelli identity, the double commutant theorem and multiplicity-free-actions.
The combinatorics of the Al-Salam-Chihara -Charlier polynomials.
The complete ellipsoidal shell-model in EEG imaging.
The continuous Jacobi transform.
The continuous Legendre transform, its inverse transform, and applications.
The Convergence Rates of Expansions in Jacobi Polynomials.
The critical values of certain Dirichlet series.
The Deformed Trigonometric Functions of two Variables
MSC 2010: 33B10, 33E20Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine...
The distribution of Mahler's measures of reciprocal polynomials.
The distributional 1F1-Transform.
The Dunkl transform.
The dynamical quantum group.
The evaluation of two-dimensional lattice sums via Ramanujan's theta functions
We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.
The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.