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Determinants play an important role in many areas of mathematics. Often, the solution of a particular problem in combinatorics, mathematical physics or, simply, linear algebra, depends on the… (More)

Using functional equations, we derive noncommutative extensions of Ramanujan's 1 ψ 1 summation. 1. Introduction. Hypergeometric series with noncommutative parameters and argument, in the special case… (More)

We give the explicit analytic development of Macdonald polynomials in terms of “modified complete” and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula.… (More)

- Andreas Ittner, Michael Schlosser
- ICML
- 1996

Most decision tree algorithms focus on uni variate i e axis parallel tests at each inter nal node of a tree Oblique decision trees use multivariate linear tests at each non leaf node This paper… (More)

Adapting a method used by Cauchy, Bailey, Slater, and more recently, the second author, we give a new proof of Bailey’s celebrated 6ψ6 summation formula.

We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting… (More)

Using Krattenthaler’s operator method, we give a new proof of Warnaar’s recent elliptic extension of Krattenthaler’s matrix inversion. Further, using a theta function identity closely related to… (More)

Abstract. In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system An. First, we apply Ismail’s [15] argument to an An q-binomial theorem… (More)

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… (More)