相关论文: Well--Poised Macdonald Functions W_lambda and Jack…

In this paper, we give various identities for the weighted average of the product of generalized Anderson-Apostol sums with weights concerning completely multiplicative function, completely additive function, logarithms, the Gamma function,…

The independent helicity amplitudes in the (Lambda_b -> \Lambda l^+ l^-) decay in the standard model and its minimal extension, i.e., with the new vector type interactions, are calculated. We calculate various asymmetry parameters…

Polarized forward-backward asymmetries in the (B_s -> l^+ l^- gamma) decay are calculated using the most general, model independent form of the effective Hamiltonian, including all possible forms of interactions. The dependencies of the…

Using the description of hypermaps with matchings, Goulden and Jackson have given an expression of the generating series of rooted bipartite maps in terms of the zonal polynomials. We generalize this approach to the case of constellations…

We use Rogers-Szego polynomials to unify some well-known identities for Hall-Littlewood symmetric functions due to Macdonald and Kawanaka.

In this article we shall study the following elliptic system with coefficients: \begin{equation}\notag \left\{\begin{aligned} -\epsilon^2\Delta u +c(x)u=b(x)|v|^{q-1}v, &\text{ and } -\epsilon^2\Delta v +c(x)v=a(x) |u|^{p-1}u &&\text{in }…

As a necessary step in constructing elliptic matrix models, which preserve the superintegrability property $<char>\sim {\rm char}$, we suggest an elliptic deformation of the peculiar loci $p_k^{\Delta_n}$, which play an important role in…

We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior…

We prove a combinatorial formula for Macdonald cumulants which generalizes the celebrated formula of Haglund for Macdonald polynomials. We provide several applications of our formula. Firstly, it gives a new, constructive proof of a strong…

A two-variable generalization of the Big $-1$ Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big $-1$ Jacobi polynomials. Their orthogonality measure is…

We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is…

Double-lepton polarization asymmetries in (Lambda_b -> Lambda l^+ l^-) decay are calculated using a general, model independent form of the effective Hamiltonian. The sensitivities of these asymmetries to the new Wilson coefficients are…

In 1996 Goulden and Jackson introduced a family of coefficients $( c_{\pi, \sigma}^{\lambda} ) $ indexed by triples of partitions which arise in the power sum expansion of some Cauchy sum for Jack symmetric functions $( J^{(\alpha )}_\pi…

The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the $q,t$-Kostka polynomials. We define operators to build standard tableaux and show that they are equivalent to creation operators…

In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action…

The well-known Jacobi elliptic functions sn(z)$, $cn(z), dn(z) are defined in higher dimensional spaces by the following method. Consider the Clifford algebra of the antieuclidean vector space of dimension 2m+1. Let x be the identity…

Analytic evaluation of Gordon's integral $$\operatorname {J}_c^{j(\pm p)}(b,b';\lambda,w,z)=\int_0^\infty x^{c+j-1}e^{-\lambda x}{}_1F_1(b;c;wx){}_1F_1(b';c\pm p;zx)dx,$$ are given along with convergence conditions. It shows enormous number…

A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from $W_\infty$ -- is that they factorize at the peculiar two-parametric topological locus in the space of time-variables, what is known as the…

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…

A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the…