Related papers: Polynomial Sequences Associated with the Moments o…
In this paper, a sequence of linear combination of $R_{I}$ type polynomials such that the terms in this sequence have a common zero is constructed. A biorthogonality relation arising from such a sequence is discussed. Besides a sequence of…
Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call `polynomial hexagon cohomologies'. Based…
In this short note, explicit formulas are developed for the central and noncentral moments of the multivariate hypergeometric distribution. A numerical implementation is provided in Mathematica for fast evaluations. This work complements…
We construct a class of permutation polynomials of $\bF_{2^m}$ that are closely related to Dickson polynomials.
We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of…
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of Bernoulli polynomials, making use of the connection between…
Making use of integral forms and superfield techniques we propose supersymmetric extensions of the multimetric gravity Lagrangians in dimensions one, two, three and four. The supersymmetric interaction potential covariantly deforms the…
The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and…
We discuss polynomials orthogonal with respect to a semi-classical generalised higher order Freud weight \[\omega(x;t,\lambda)=|x|^{2\lambda+1}\exp\left(tx^2-x^{2m}\right),\qquad x\in\mathbb{R},\] with parameters $\lambda > -1$,…
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity.…
This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
We prove hypergeometric type summation identities for a function defined in terms of quotients of the $p$-adic gamma function by counting points on certain families of hyperelliptic curves over $\mathbb{F}_{q}$. We also find certain special…
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, it gives an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations,…
We compute explicit formulae for the moments of the densities of the eigenvalues of the classical $\beta$-ensembles for finite matrix dimension as well as the expectation values of the coefficients of the characteristic polynomials. In…
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and…
In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.