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...

Two new species, Sarcophaga (Sarcosolomonia) collessi sp.nov. and Sarcophaga (Sarcorohdendorfia) clavus sp.nov., both collected in Queensland, Australia, are described, and the following four new synonymies are proposed: Sarcophaga horti Blackith and Blackith, 1988 syn.nov. of Sarcophaga bancroftorum Johnston and Tiegs, 1921; Sarcophaga fergusonina Hardy, 1940 syn.nov. of Sarcophaga assimilis M...

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.

A new type of polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.

We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity, Theorem 2.2, gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities. Several examples of new Rogers-Ramanujan type identities are given.