Re: What is QGamma[q,z]

*To*: mathgroup at smc.vnet.net*Subject*: [mg95554] Re: [mg95503] What is QGamma[q,z]*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 21 Jan 2009 06:47:53 -0500 (EST)*References*: <200901201047.FAA16820@smc.vnet.net>

On 20 Jan 2009, at 11:47, Ted Ersek wrote: > Q function are new in Mathematica 7. > What applications are there for these things? > Also I can't understand the definition of these things because the > Mathematica documentation uses notation I never herd of. > Could sombody explain the definition of QGamma[q,z] in terms of > functions I am likely to know about. > > Thanks, > Ted Ersek > > No, they cannot be explained "in terms of" you are likely to know about but they are analogues of the functions you surely know about (the ones without the q). The classical ones correspond to q=1. The starting point is the q-binomial theorem and the q-Pascal Triangle, which is pretty well explained here: http://demonstrations.wolfram.com/QPascalTriangle/ You might also look at this: http://demonstrations.wolfram.com/QTrigonometricFunctions/ These things are quite useful, both in pure mathematics (e.g. the so called Ramanujan's Summation formula) and in physics in connection with quantum theory. Also, the q-binomial coefficients have a nice geometric interpretation in terms of areas under lattice paths due to Polya, but all of this would take too long to describe here. If I can find the time for it I will make a Mathematica Demonstration of Polya's interpretation of the q-Binomial Theorem some day, but I it won't happen very soon (perhaps someone else might want to do it earlier). Anyway, all of this is described in the classic text:Andrews,Askey,Roy "Special Functions", Chapter 10. Andrzej Kozlowski

**References**:**What is QGamma[q,z]***From:*"Ted Ersek" <ersekt@md.metrocast.net>