That's the q-pochhammer symbol: (c1224) BLOCK([FANCY_DISPLAY : FALSE],QPOCH(A,B,C,Q^2,N),STRINGPOCH(%%) = MAKEPROD(%%)) n - 1 /===\ 2 | | 2 i 2 i 2 i (d1224) (a,b,c;q ) = | | (1 - a q ) (1 - b q ) (1 - c q ) n | | i = 0 I should also re-mention that there's a polynomial relating pi_q, pi_q^2, and pi_q^4 that Gene Salamin turned into a quadratic algorithm for pi. --- On Thu, 6/12/08, Mike Stay <metaweta@gmail.com> wrote:
From: Mike Stay <metaweta@gmail.com> Subject: Re: [math-fun] Missing Catalan identity To: "math-fun" <math-fun@mailman.xmission.com> Date: Thursday, June 12, 2008, 10:41 AM On Thu, Jun 12, 2008 at 4:15 AM, <rwg@sdf.lonestar.org> wrote:
Mike Stay> What's the definition of q-deformed pi, pi_q?
Just take that infinite product following (d37) as the definition--it's a q-extension of Wallis's product. (-> pi as q -> 1).
Can you remind me how the semicolon notation works? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com