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Re: Fwd: Re: what actually is in the WRI "functions" database?
I had no idea that someone scanned A&S pages. It seems obvious in retrospect, with web hosting and scanning being so cheap, and the book being public domain. There are undoubtedly different versions of formulas with different levels of usefulness. Perhaps what the functions web site should do is work more closely with DLMF. Why should I believe Michael Trott's assertion that some standard-form formula is correct? Who does he think he is, Stephen Wolfram? :) And the Mathematica formulas that he knows to be wrong are not even marked as wrong (or inadequately encoded). This is, to me, quite unacceptable. Excuses after the fact like "this will have to do until a better encoding comes along in a future Mathematica" or "MathML doesn't have the expressive capacity for this" are not adequate rationals to provide known erroneous formulas. I don't understand how this could even be controversial. If something is semantically meaningless, you don't just hand it to someone without mentioning this fact. If Lozier and his DLMF team say a formula is correct, it could still be wrong, but at least we have some idea that it has been checked over by an official "team" of experts. Yet I have expressed my disappointment with the DLMF project to Lozier and others, not only on the time scale, but the general lack of ambition. I have pointed out to them the possibility of having more of a "live" aspect, and in a talk at NIST (years ago) I had slides of pages from the functions.wolfram site. If NIST were to do something like this, it would have more authority, being "vendor independent" and might be optionally attached to one (or more) CAS. Some might even be on-line, live, and free. G&R has been checked over by many people. It may still have mistakes, but there have been many eyes looking at it. For a long time. And it has cross references. And the latest version, edited by Dan Zwillinger, was generated from a macro language with an expansion into live CAS language (Mathematica, I think.) While the concept, the typography, and the scope of functions.wolfram is admirable, the content seems to be untrustworthy, so what's the point? [You may say, just as G&R accept reports of errors, so can the web site --- yes, this is an important positive aspect of the on-line repository. Will Michael Trott fix the broken formulas that I have reported? Will he go through all formulas with ellipsis and mark the InputForm somehow? I hope so.] RJF