If x (log x) = y, then, asymptotically, x ~= y / log y. Even closer, x ~= y / (log y - loglog y), and x ~= y / (log y - log(log y - ...)). This particular problem can also be written with the Lambert W function, but it brings up a general problem: It wouldn't hurt us to have some standard algebra for representing these ideas, expressions, and implied computations. Obviously the new stuff would have to come with some caveats about how to manipulate it and when it works, but we already cope with sqrt, cbrt, log, and sin^-1, and have internalized the rules about when to be careful with simplifying & rearranging. There's no good reason that formulas using the inverse function for x(log x) should require a dependent clause. It just makes understanding them harder. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of dasimov@earthlink.net Sent: Wed 3/1/2006 8:59 AM To: math-fun Subject: Re: [math-fun] Stirling Numbers? Thanks, everyone, for the interesting asymptotic expressions for B(n). (Would only that they were expressed purely in terms of n, rather than a root of some weird equation in n.) --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun