Related papers: On a problem of Bart Goddard

Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in Yanigian are discussed. As a corollary, similar relations are deduced for shifted Schur functions.

Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…

We characterise all pairs of finite order entire functions whose magnitudes agree on two arbitrary lines in the complex plane by means of the Hadamard factorisation theorem. Building on this, we also characterise all pairs of second order…

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.

The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummer's summation theorem obtained earlier by Rakha and…

For a family of holomorphic functions on an arbitrary domain, we introduce Fatou and Julia like sets, and establish some of their interesting properties.

Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…

The main result of this paper is two infinity classes of series-product identities which is based on classical Gauss identity and two different interpretations of character formula for irreducible highest weight modules of affine Lie…

We extend our investigation of $2$-determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous…

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…

The paper introduces a new concept of $\Lambda $-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series

Our present investigation is motivated essentially by the fact that, in Geometric Function Theory, one can find many interesting and fruitful usages of a wide variety of special functions and special polynomials. The main purpose of this…

According to the method of series rearrangement, we establish the extensions of two $q$-Gosper identities with an extra integer parameter. The limiting cases of them produce the generalizations of Gosper's two $_3F_2(\frac{3}{4})$-series…

In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose parts are separated by parity, and we prove various $q$-series…

We define a series $\mathcal{F}_{M,N}$ as a certain generalization of $q$-hypergeometric function. We study its duality and the system of $q$-difference nonlinear equations which admits particular solutions in terms of $\mathcal{F}_{1,M}$.

Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a family of series containing fourth powers of Catalan numbers.…

Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.