On A Generalization Of Humbert Polynomials
On a generalization of Humbert polynomials.
On a generating function of ultraspherical polynomals.
S. K. Chatterjea has recently proved a class of generating relations involving ultraspherical polynomials from the view point of continuous transformations-groups. The object of the present paper is to point out that this class of generating relations implies the explicit representation, the addition and the multiplication formulas, in addition to the usual generating relation for the ultraspherical polynomials.
On a New Class of Polynomial set Suggested by Hermite Polynomials
On a new set of orthogonal polynomials
An orthogonal system of polynomials, arising from a second-order ordinary differential equation, is presented.
On a positive sine sum
On a q-deformed harmonic oscillator with variable linear momentum.
On Abel summability of multiple Jacobi series
On a.e. convergence of expansion with respect to a bounded orthonormal system of polygonals
On an irreducibility theorem of I. Schur
On Appel-type quadrature rules.
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 certain formulas of Karlin and Szegö.
On certain generating functions for Laguerre polynomials
On certain subclass of Bazilevič functions.
On certain theorems in transform calculus.
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 Eulerian integrals of the first and second kind associated with multiple hypergeometric series
On generalisation of polynomials in complex plane.