Related papers: An elementary approach to 6j-symbols (classical, q…
This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
For each generic $(3\mbox{-}j)$ the column parities, $2(j \pm m)$, define $3$ intrinsic parities: $\alpha, \beta,\gamma$. In algebra $so(3)$ only $(3\mbox{-}j)\_{\alpha}$ exists whereas super-algebra $osp(1|2)$ admits $3$ kinds of…
We derive the leading asymptotic limit of the Wigner $3j$-symbol from a stationary phase approximation of a twelve dimensional integral, obtained from an inner product between two exact Bargmann wavefunctions. We show that, by the…
We define quantum W-algebras generalizing the results of Reshetikhin and the second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated to sl_N is an associative algebra depending on two parameters. For special values…
This paper presents a neurosymbolic approach to classifying Galois groups of polynomials, integrating classical Galois theory with machine learning to address challenges in algebraic computation. By combining neural networks with symbolic…
We state and discuss numerous mathematical identities involving Jacobi elliptic functions sn(x,m), cn(x,m), dn(x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either…
In this paper we construct a light-like polygonal Wilson loop in N=6 superspace for ABJM theory. We then use it to obtain constraints on its two- and three-loop bosonic version, by focusing on higher order terms in the $\theta$ expansion.…
Outer Billiards is a geometrically inspired dynamical system based on a convex shape in the plane. When the shape is a polygon, the system has a combinatorial flavor. In the polygonal case, there is a natural acceleration of the map, a…
Dodgson polynomials appear in Schwinger parametric Feynman integrals and are closely related to the well known Kirchhoff (or first Symanzik) polynomial. In this article a new combinatorial interpretation and a generalisation of Dodgson…
A class of elliptic curves with associated Lax matrices is considered. A family of dynamical systems on e(3) parametrized by polynomial a with above Lax matrices are constructed. Five cases from the family are selected by the condition of…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction and restriction functor. These sub-coalgebras have as…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
This paper aims to initialize a dynamical aspect of symbolic integration by studying stability problems in differential fields. We present some basic properties of stable elementary functions and D-finite power series that enable us to…
Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and…
We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic…
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…
There are two types of asymptotic formulas for the $12j$ symbol with one small and 11 large angular momenta. We have derived the first type of formula previously in [L. Yu, Phys. Rev. A84 022101 (2011)]. We will derive the second type in…