相关论文: Hypergeometric solutions of some algebraic equatio…

We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric…

We systematically describe and classify 1-dimensional Schr\"odinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new classes of exactly solvable…

We give an overview of some of the main results from the theories of hypergeometric and basic hypergeometric series and integrals associated with root systems. In particular, we list a number of summations, transformations and explicit…

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…

This paper is dedicated to provide theta function representations of algebro-geometric solutions for the Fokas-Lenells (FL) hierarchy through studying an algebro-geometric initial value problem. Further, we reduce these solutions into…

We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational…

We review some general and recent results on the characterization and construction of timelike supersymmetric solutions of 4-dimensional supergravity theories.

We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent…

We give a formula computing the irregular Hodge numbers for a confluent hypergeometric differential equation.

In this paper, we establish a curvature estimate for semi-convex solutions of Hessian equations in hyperbolic space. We also obtain a curvature estimate for admissible solutions to prescribed curvature measure type problem in hyperbolic…

By building a second order adjoint difference equations on nonuniform lattices, the generalized Rodrigues type representation for the second kind solution of a second order difference equation of hypergeometric type on nonuniform lattices…

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

In this paper we show that it is possible to project onto the solutions of the $\mathfrak{grt}$ hexagon equation. We also consider in some sense generalized hexagon equations and other symmetry equations for multiple argument maps between…

This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple…

We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.

Using the representation of the isometries as 2x2 invertible matrices over the division algebra $\H$ of quaternions, we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic…

A completely algebraic treatment of the six-dimensional hypercoulomb problem is discussed in terms of an oscillator realization of the dynamical algebra of SO(7,2). Closed expressions are derived for the energy spectrum and form factors.

We solve connection problem between fundamental solutions at singular points $0$ and $1$ for the generalized hypergeometric function, using analytic continuation of the integral representation. All connection coefficients are products of…

We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems A_n, C_n and D_n. In the special cases of classical and q-series, our approach leads to new elementary proofs of the…

In this paper, we obtain analytical solutions of Laplace transform based some generalized class of the hyperbolic integrals in terms of hypergeometric functions ${}_3F_2 (\pm1)$, ${}_4F_3 (\pm1)$, ${}_5F_4(\pm1)$, ${}_6F_5(\pm1)$,…