Recently, starting from two infinite summation formulae for Hall-Littlewood polynomials, two of the present authors [7] have generalized a method due to Macdonald [9] to obtain new finite summation formulae for these polynomials. This approach permits them to extend Stembridge’s list of multiple qseries identities of Rogers-Ramanujan type [12]. Conversely these symmetric functions identities ca...

The impact of import competition on labour productivity is examined using panel data for a sample of Australian manufacturing firms over the period 1984 to 1993. Import competition is found to interact with domestic competition; such the positive impact of import competition on the level and rate of growth of labour productivity rises with the degree of concentration among domestic producers. T...

Describing the elementary theories of Rogers semilattices is one of the main problems of the theory of numberings. For the classical case of computable families of computably enumerable sets, V.V. V’jugin showed in [1] the existence of infinitely many families with pairwise elementarily different Rogers semilattices. Nevertheless, the study of Rogers semilattices undertaken in recent years (see...

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) andK(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan’s forty identities for Rogers-Ramanujan function...

We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson’s transformation formula by specialization or through Bailey’s method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.