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Full-Text Articles in Physical Sciences and Mathematics
Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Mathematics Faculty Publications
In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey pairs, a theorem of Watson on basic hypergeometric series, generating functions and miscellaneous methods.
Lifting Bailey Pairs To Wp-Bailey Pairs, James Mclaughlin, Andrew Sills, Peter Zimmer
Lifting Bailey Pairs To Wp-Bailey Pairs, James Mclaughlin, Andrew Sills, Peter Zimmer
Mathematics Faculty Publications
A pair of sequences (αn(a,k,q),βn(a,k,q)) such that α0(a,k,q)=1 and βn(a,k,q)=∑nj=0(k/a;q)n−j(k;q)n+j(q;q)n−j(aq;q)n+jαj(a,k,q) is termed aWP-Bailey Pair . Upon setting k=0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WP-Bailey pair, and use some of the new WP-Bailey pairs found in this way to derive some new identities between basic hypergeometric series and new single-sum and double-sum identities of the Rogers–Ramanujan–Slater type.
Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills
Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills
Mathematics Faculty Publications
We provide the missing member of a family of four q-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered inIdentities of the Ramanujan-Slater type related to the moduli 18 and 24.
Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer
Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer
Mathematics Faculty Publications
We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers–Ramanujan type and identities of false theta functions.