On Appel-type quadrature rules.
On asymptotics of discrete Mittag-Leffler function
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional -difference operators) and describe its...
On asymptotics of the maximum likelihood scale invariant estimator of the shape parameter of the gamma distribution
The maximum likelihood scale invariant estimator of the shape parameter of the gamma distribution, proposed by the authors [Statist. Probab. Lett. 78 (2008)], is considered. The asymptotics of the mean square error of this estimator, with respect to that of the usual maximum likelihood estimator, is established.
On automorphic L-functions for the Jacobi group of degree one and a relation with L-functions for Jacobi forms.
On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms
We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.
On b-function, spectrum and rational singularity.
On block recursions, Askey's sieved Jacobi polynomials and two related systems
Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.
On bounds for the characteristic functions of some degenerate multidimensional distributions.
On calculation of zeta function of integral matrix
Values of the Epstein zeta function of a positive definite matrix and the knowledge of matrices with minimal values of the Epstein zeta function are important in various mathematical disciplines. Analytic expressions for the matrix theta functions of integral matrices can be used for evaluation of the Epstein zeta function of matrices. As an example, principal coefficients in asymptotic expansions of variance of the lattice point count in the random ball are calculated for some lattices.
On certain congruences for Fourier coefficients of classical cusp forms
On Certain Definite Integrals.
On certain formulas for the multivariable hypergeometric functions.
On certain formulas of Karlin and Szegö.
On certain generating functions for Laguerre polynomials
On certain Heun functions, associated functions of discrete variables, and applications.
On certain inequalities involving the Lambert W function.
On certain operational formula for multivariable basic hypergeometric functions.
On certain properties of Hankel transform
On certain subclass of Bazilevič functions.
On certain sufficient condition involving Gaussian hypergeometric functions.