Two new multivariable generating relations

A New Multivariable

Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson’s 8φ7 summation formula by Milne, a new multivariable 8φ7 summation is derived. By a polynomial argument this 8φ7 summation is transformed to another multivariable 8φ7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6φ5 summation. The latter is ...

New relations for two-dimensional Hermite polynomials

The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for large values of indices are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.

Recurrence Relations and Generating Functions

Generating Referring Expressions Involving Relations

In this paper we review Dale s algorithm for determining the content of a referring expres sion The algorithm which only permits the use of one place predicates is revised and extended to deal with n ary predicates We investigate the problem of blocking recursion in complex noun phrases and propose a solution in the context of our algorithm

Generating Relations from XML Documents

This paper discusses several mechanisms for creating relations out of XML documents. A relation generator consists of two parts: (1) a tuple of path expressions and (2) an index indicating which path expressions may not be assigned the null value. Evaluating a relation generator involves finding tuples of nodes that satisfy the path expressions and are related to one another in a meaningful fas...