The q-gamma function for x<0.
The quantized Jacobi polynomials
The author studies a system of polynomials orthogonal at a finite set of points its weight approximating that of the orthogonal system of classical Jacobi polynomials.
The Rahman polynomials are bispectral.
The rate of convergence for spectra of GUE and LUE matrix ensembles
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
The rational qKZ equation and shifted non-symmetric Jack polynomials.
The reciprocal of the beta function and Whittaker functions
In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself.We then apply our new formula to the study of Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral representations of “fundamental”...
The relational translators of the hyperspherical functional matrix.
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The representation and the approximation of one class of exponential functions
The restricted Toda chain, exponential Riordan arrays, and Hankel transforms.
The roots of the third J. Jckson -Bessel function.
The second-order Klein-Gordon field equation.
The second-order self-associated orthogonal sequences.
The sharpness of convergence results for -Bernstein polynomials in the case
Due to the fact that in the case the -Bernstein polynomials are no longer positive linear operators on the study of their convergence properties turns out to be essentially more difficult than that for In this paper, new saturation theorems related to the convergence of -Bernstein polynomials in the case are proved.
The special function ش
The special function ش , II
The special function ش , III
The Spectrum of Hill's Equation.
The spt-crank for overpartitions
Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions , , , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...
The structure of totally disconnected, locally compact groups.