相关论文: Contiguous relations, continued fractions and orth…

The main result of this paper is a recursive description of all decompositions \[ \Delta^+ = \Phi_1 \sqcup \Phi_2 \sqcup \dots \sqcup \Phi_k \] of the positive roots $\Delta^+$ of an arbitrary root system $\Delta$ into a disjoint union of…

We give a complete criterion for when two hyperbolic automorphisms of a tree generate a free, discrete subgroup. The decision depends only on three geometric invariants: the translation lengths of the generators and the length of overlap of…

The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These have been widely studied in the case of the torsion-free,…

Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…

Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…

By making use of the multiplicate form of the extended Carlitz inverse series relations, we establish two general `dual' theorems of Jackson's summation formula for well--poised $_8\phi_7$-series. Their duplicate forms under the partition…

We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group. By computing the radial part of a…

Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric…

The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the…

Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $\Phi:M\to so(3)$. The pair $(A,\Phi)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge…

We study self-similar sets and measures on $\mathbb{R}^{d}$. Assuming that the defining iterated function system $\Phi$ does not preserve a proper affine subspace, we show that one of the following holds: (1) the dimension is equal to the…

We introduce a family of 3-variable "Farey polynomials" that are closely connected with the geometry and topology of $3$-manifolds and orbifolds as they can be used to produce concrete realisations of the boundaries and local coordinates…

In this paper, we prove several transformation formulas for the very-well-poised bilateral basic hypergeometric $_5\psi_5$ series by using the relationship between the bilateral basic hypergeometric $_5\psi_5$ series and basic…

Rational approximations of generalized hypergeometric functions ${}_pF_q$ of type $(n+k,k)$ are constructed by the Drummond and factorial Levin-type sequence transformations. We derive recurrence relations for these rational approximations…

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…

Using contiguous relations we construct an infinite number of continued fraction expansions for ratios of generalized hypergeometric series 3F2(1). We establish exact error term estimates for their approximants and prove their rapid…

In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…

A result of P\'olya states that every sequence of quadrature formulas $Q_n(f)$ with $n$ nodes and positive numbers converges to the integral $I(f)$ of a continuous function $f$ provided $Q_n(f)=I(f)$ for a space of algebraic polynomials of…

Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables…