160 research outputs found
New Finite Rogers-Ramanujan Identities
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.Comment: 19 pages. to appear in Ramanujan
Rogers-Ramanujan Computer Searches
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
Explicit Forms and Proofs of Zagier's Rank Three Examples for Nahm's Problem
Let be a positive integer, a real positive semi-definite
symmetric rational matrix, a rational vector of length , and
a rational scalar. Nahm's problem is to find all triples such
that the -fold -hypergeometric series
becomes a modular form, and we call such a modular
triple. When the rank , after extensive computer searches, Zagier provided
twelve sets of conjectural modular triples and proved three of them. We prove a
number of Rogers-Ramanujan type identities involving triple sums. These
identities give modular form representations for and thereby verify all of
Zagier's rank three examples. In particular, we prove a conjectural identity of
Zagier.Comment: 37 pages. We made some changes after the first version. Comments are
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