A representation of Sheffer polynomials in terms of a differential equation for their generating functions. (Short Communication).
A restricted Epstein zeta function and the evaluation of some definite integrals
A series transformation formula and related polynomials.
A set of orthogonal polynomials induced by a given orthogonal polynomial.
A sextuple product identity with applications.
A sharp inequality involving the psi function.
A Short Proof of Selberg's Generalized Beta Formula.
A simple method for constructing non-liouvillian first integrals of autonomous planar systems
We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
A simple proof of Ramanujan's summation of the ... .
A simplification of the Laplace method for double integrals. Application to the second Appell function.
A sixteenth-order polylogarithm ladder.
A solution of the boundary value problem in heat conduction
A special class of two dimensional exponential-Bessel series of Fox’s -function
A study of -Laguerre polynomials through the -operator
The present paper deals with certain generating functions and recurrence relations for -Laguerre polynomials through the use of the -operator introduced in an earlier paper [7].
A survey on D-semiclassical orthogonal polynomials.
A symbolic operator approach to power series transformation-expansion formulas.
A system of differential equations for the Airy process.
A transformation formula for a special bilateral basic hypergeometric series.
A transplantation theorem for ultraspherical polynomials at critical index
We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the “boundary” Lorentz space corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients of -functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any the series is the Fourier series of some function φ ∈ ReH¹ with .
A triple lacunary generating function for Hermite polynomials.