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.
On certain theorems in transform calculus.
On certain transcendental functions
On Chebyshev's polynomials and certain combinatorial identities.
On classifying Laguerre polynomials which have Galois group the alternating group
We show that the discriminant of the generalized Laguerre polynomial is a non-zero square for some integer pair , with , if and only if belongs to one of explicitly given infinite sets of pairs or to an additional finite set of pairs. As a consequence, we obtain new information on when the Galois group of over is the alternating group . For example, we establish that for all but finitely many positive integers , the only for which the Galois group of over is is .
On Clenshaws's Method and a Generalisation to Faber Series.