His topics include the q-binomial theorem, Heine's transformation, the Jacobi triple product
identity, the Rogers-Fine identity, Bailey chains, WP-Bailey pairs and chains, further results on Bailey/WP-Bailey pairs and chains, bijective proofs of basic hypergeometric identities, q-continued fractions, Lambert series, and mock theta functions.
Above this value (the so-called "triple product
"), the energy released in a reactor exceeds the energy required to keep the reaction going.
At the end of Q1, penetration of triple product
customers increased to 36% compared to 33% in the first quarter of 2013.
Equation (5) indicates [x.sub.k,n,p] as a sum of triple products
, which is variably known as the trilinear model, trilinear decomposition, triple product
decomposition, canonical decomposition, or parallel factor (PARAFAC) analysis.
With above notation, the celebrated Jacobi triple product
identity can be expressed as follow
An invitation to q-series; from Jacobi's triple product
identity to Ramanujan's "most beautiful identity".
Jacobi's triple product
identity (JTP) is ubiquitous in various areas of mathematics and especially in analytical number theory.
Thanks to this triple product
registration in the EU, Novus is confident that it will repeat the Brazilian and US successes of the MINTREX[R] range in Europe.
"It is going to triple product
development budgets and we are doubling our number of research and development engineers.
In this paper, we obtain a new proof of Ramanujan's receprocity theorem using an Heine's transformation which is a generalization of Jacobi's triple product
The lowest order I-violating combination of spins and momenta appears in the form of the mixed triple product
. From the experimentally accessible quantities, four triple products
can be formed: R J * (p X s), D J * (p X [p.sub.v]), V J * (P X s), L P * (p X s), where J is the spin of the parent system, s, p are the spin and momentum of the detected lepton, P denotes the momentum of the recoil system and [p.sub.v] stands for the momentum of the unobserved neutrino.
But the triple product
of energy, confinement time and density--the three critical parameters -- is 10 to 20 times that of DCX-1, and none of the typical instabilities formed.