An algorithm for free algebras
We present an algorithm for constructing the free algebra over a given finite partial algebra in the variety determined by a finite list of equations. The algorithm succeeds whenever the desired free algebra is finite.
An algorithmic proof theory for hypergeometric (ordinary and "q") multisum/integral indentities.
An alternative definition of the Hermite polynomials related to the Dunkl Laplacian.
An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative
Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...
An analogue of a problem of J. Balázs and P. Turán, II (Inequalities)
An analogue of the Gauss summation formula for hypergeometric functions related to root systems.
An analytic formula for the Jack polynomials.
An Apéry-like difference equation for Catalan's constant.
An Application for the Chebyshev Polynomials
An application of fractional calculus
An application of hypergeometric functions to a problem in function theory.
An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions.
We shall establish full asymptotic expansions for the mean squares of Lerch zeta-functions, based on F. V. Atkinson's device. Mellin-Barnes' type integral expression for an infinite double sum will play a central role in the derivation of our main formulae.
An application of shift operators to ordered symmetric spaces
We study the action of elementary shift operators on spherical functions on ordered symmetric spaces of Cayley type, where denotes the multiplicity of the short roots and the rank of the symmetric space. For even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on by a reduction to the rank 1 case. Finally we generalize our notions and results to type root systems.
An application of the generalized Bessel function
We introduce and study some new subclasses of starlike, convex and close-to-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.
An approximation for the zeros of Bessel functions.
An asymptotic confluent expansion for certain functions of several variables
An asymptotic expansion for a ratio of products of gamma functions.
An asymptotic expansion for the Catalan-Larcombe-French sequence.
An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials.
An elementary approach to the hypergeometric shift operators of Opdam.