Related papers: A generalization of complete and elementary symmet…
In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…
The Newton-Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have…
In this paper, we define extended trigonometric functions via series and employ the method of contour integration to investigate the parity of certain cyclotomic Euler sums and multiple polylogarithm function. We can provide the statement…
We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential…
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
We provide an explicit description of the quantum product of multi-symmetric functions using the elementary multi-symmetric functions introduced by Vaccarino.
Snakes are analogues of alternating permutations defined for any Coxeter group. We study these objects from the point of view of combinatorial Hopf algebras, such as noncommutative symmetric functions and their generalizations. The main…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
We study a multi-symmetric generalization of the classical Schur functions called the multi-symmetric Schur functions. These functions form an integral basis for the ring of multi-symmetric functions indexed by tuples of partitions and are…
We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
We give a combinatorial extension of the classical inequalities of Maclaurin about symmetric functions of several variables. We discuss two problems - one analytical and another combinatorial - and show that they are in some sense…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…