Том 71
№ 11

All Issues

Chu W.

Articles: 2
Article (English)

Iteration process for multiple Rogers-Ramanujan identities

Chu W., Wang C.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 100-125

Replacing the monomials by an arbitrary sequence in the recursive lemma found by Bressoud (1983), we establish several general transformation formulas from unilateral multiple basic hypergeometric series to bilateral univariate ones, which are then used for the derivation of numerous multiple series identities of Rogers-Ramanujan type.

Article (English)

Well-posed reduction formulas for the $q$-Kampé-de-Fériet function

Chu W., Zhang W.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 11. - pp. 1538–1554

By using the limiting case of Watson’s $q$-Whipple transformation as $n → ∞$, we investigate the transformations of the nonterminating $q$-Kampé-de-Fériet series. Further, new formulas for the transformations and well-posed reduction formulas are established for the basic Clausen hypergeometric series. Several remarkable formulas are also found for new function classes beyond the $q$-Kampé-de-Fériet function.