GarethM>On Monday 22 October 2012 01:10:18 Mike Speciner wrote:

Well, maybe I'm just too fussy. (My first job, in the early '70s, was> writing software to typeset mathematics beautifully, and I always> thought that TeX was a big step backwards from the state of the art.)> Your png looks quite similar to what I see. Should I not expect the> first two 1s to be at the same height? Should I not expect the ; between> 1/qz and 1/q to be vertically centered around the fraction bars so that> the semicolon's dot doesn't look like a center dot? And should I not> expect the spacing to be a bit looser in several places?

I'm fairly sure that texify.com is not in fact running TeX; it's doing some simpler cheaper thing, probably involving MathML or something. If you typeset that same formula in TeX then ... well, actually you still get something pretty ugly, but it's ugly in quite different ways. What was the state of the art of computerized mathematical typesetting before TeX? -- g ----------- Well, at Stanford AI there was P(rototype)O(verlay)X(erographics). The macrology was an absolute bear. For a quotient, you had to measure the numerator and denominator, max for the division bar, and do your own centering. I wrote my own list mapper. The simplest call required six consecutive open parens. I just restored <http://gosper.org/facfun.pdf> (scanned XGP output, pre-inkjet, pre-laser) from a server crash. --rwg MRob>What is the date (year of authorship) of these ancient (mostly) POX notes? I want to add this as a reference for OEIS sequence A2109:https://oeis.org/A002109 ------------------------- There's a handwritten letter in the binder dated 1979. It must have coincided with the dawn of TeX, since the later pages are TeXed. MRob> It would also be nice to add a sequence for the (Gosper's) second factorial with integer arguments, which I take to be 1, 1, 16, 122009559759792, 16358..68032 (169 digits, approx. 1.63588 x 10 ^ 168) but I don't like to add sequences without a reference. - Robert [Munafo] I'm sure there are better references, but J.W.L. Glaisher uses the function on p81-87 of Products and series involving prime numbers only, part II, The Quarterly Journal of Pure and Applied Mathematics, Vol. XXVIII and on p82 refers to an apparently more relevant article in The Messenger of Mathematics, Vol XXIII, p155, presumably also by Glaisher. I haven't checked, but I suspect his ilg_2 function is the closely related double integral of log gamma. (A negapolygamma.) Glaisher also treats prod k^k^n, n<0. Barnes and Kinkelin and perhaps Alexiewsky(sp?) almost certainly treated this function. --rwg On 5/7/12, Bill Gosper <billgosper@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com> <http://www.gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> wrote:> By way of preservation, Neil has kindly scanned in my ancient,> (mostly) POX (pre-Tex), brief notes <http://gosper.org/facfun.pdf>> (3.7M) on higher factorials.> These stem from my astounding discovery that the dot at the> bottom of an exclamation point is actually hollow, representing> the number 0, and what happens when you change it to a 1.> --rwg On the subject of shapes with constant dissolution rates, there might be real monetary incentive from the drug companies, seeking to improve "timed release". To illustrate the lengths they've already reached, I take an expensive, insoluble plastic pill with a laser-punched pinhole, through which medication is pushed by a tiny expanding sponge. There must already be scads of patents on inhomogeneous pills, with solubility varying with internal depth, etc.