Define oo /===\ i | | 1 - a q (a; q) := | | ------------, x | | x + i i = 0 1 - a q a product of |x| binomials when x is an integer. By Mathematica, 2 3 3 3 (a; q) = (a q ; q ) (a; q ) (a q; q ) 3 n n - 1/3 n n + 1/3 3 5 4 5 5 (a; q) = (a q ; q ) (a q ; q ) (a; q ) 5 n n - 2/5 n - 1/5 n 5 2 5 (a q; q ) (a q ; q ) n + 1/5 n + 2/5 4 5 2 5 5 3 5 = (a q ; q ) (a q ; q ) (a; q ) (a q ; q ) n - 2/5 n - 1/5 n n + 1/5 5 (a q; q ) n + 2/5 4 5 3 5 5 2 5 = (a q ; q ) (a q ; q ) (a; q ) (a q ; q ) n - 3/5 n - 1/5 n n + 1/5 5 (a q; q ) n + 3/5 What's likely to be the case for 7? 2, 4, and 6? --rwg BRAINSTEM TRIBESMAN b jdb@math.arizona.edu aka@pu.ac.in hic@iname.com aadler@sbcglobal.net misha@nasledov.com aaronl@vitelus.com srinivasamu rthyb@yahoo.com rjpetti@rcn.com jeffrey.golden@verizon.net fateman@cs.berkeley.edu djeffrey@uwo.ca Rob.Corless@uwo.ca ch ongo@mellis.com mikeh@maths.unsw.edu.au AnneStrass@aol.com cshapiro@panix.com whitfield.diffie@Sun.COM gregaleg909@yahoo .com ono@math.wisc.edu tjhuber@math.uiuc.edu ruiming_zhang@hotmail.com b elh@osots.com rudy@rudyrucker.com silver@pilgrim.com sk@pilgrim.com peter7387@aol.com rwellessprint@earthlink.net b danny@appliedminds.com meryt@worldnet.att.net djeffrey@uwo.ca Rob.Corless@uwo.ca smj@cirr.com thomasmrodgers@yahoo.com mtrott@wolfram.com oleg@wolfram.com pavlyk@wolfram.com countolaf148@hotmail.com