I haven't read Borwein & Borwein, and I don't know much about the AGM beyond its definition. (Or one def. at least: for a,b > 0 define F(a,b) := ((a+b)/2, sqrt(ab)) and iterate; the limit is then (AGM(a,b), AGM(a,b)) if memory serves.)* Is much known about when AGM(a,b) is rational, algebraic, or transcendental? --Dan ___________________________________ * Btw, is there a natural continuum of "means" with the AM & GM at the extremes, and the AGM halfway between them? _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele