9 research outputs found
On WZ-pairs which prove Ramanujan series
The known WZ-proofs for Ramanujan-type series related to gave us the
insight to develop a new proof strategy based on the WZ-method. Using this
approach we are able to find more generalizations and discover first WZ-proofs
for certain series of this type.Comment: 12 pages (preprint) + 1 page (addendum). The addendum (A Maple
program) is not in the Journal referenc
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
Two Definite Integrals That Are Definitely (and Surprisingly!) Equal
Contains fulltext :
225681.pdf (publisher's version ) (Open Access
q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem
We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berkovich, and Berkovich and Garvan
âRussian killerâ no. 2: A challenging geometric theorem with human and machine proofs
Creative Telescoping for Holonomic Functions
Abstract The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified. On the other hand, this chapter has the flavour of a survey article: the developments in this area during the last two decades are sketched and a selection of references is compiled in order to highlight the impact of creative telescoping in numerous contexts.