What I first encountered was rather sobering, as it was soon apparent that I was in way over my head
The National Institute of Standards and Technology (NIST) recently released five preview chapters of its online Digital Library of Mathematical Functions (DLMF). This is supposedly a definitive reference work on special functions (those that frequently occur in mathematical modeling of physical phenomena) in applied mathematics. An Internet announcement said that it was in development for over a decade and that the final product, of 36 chapters, will be the successor to its 1964 ‘Handbook of Mathematical Functions,’ a popular reference work. It is also stated that the preview is a fully functional beta-release of the full version, expected to be released in early 2009.
Well, five chapters are enough to give anyone a flavor of its usefulness, and I approached the exercise in learning as someone new to the DLMF and a very novice mathematician. What I first encountered was rather sobering, as it was soon apparent that I was in way over my
head. Indeed, the help section had a choice called “It all looks all greek to me” offering excellent advice. The first sentence read “Well, it could be that you need to take more math courses!’. The authors meant this to be humorous but, in many cases, it may be right to the point! As the work comes from NIST, I’m assuming that it is targeted largely toward engineers and physicists. I know many industrial engineers are now employed in other areas and this would be quite a challenge to them. As to the chemists and biologists, it would be even more severe a stretch!
I found the initial content (asymptotic approximations) as stiff and as “useful” as my copy of the Oxford User’s Guide to Mathematics, and at least that had plenty of verbiage in the later chapters to shed some light on what was happening. Too many terse and compact numerics send me running back to my copy of The CRC Handbook of Chemistry and Physics! At least I’m familiar with the content and can pick my way through some derivations. I didn’t find many of the features supposedly present, such as the interactive web tools for 3-D visualization, the mouse-over feature or the ‘click on the function to get a more complete explanation’. In all fairness, however, the level of chapter difficulty was uneven, a reflection of the underlying mathematics.
I was delighted to find an old friend, number theory, in the index. Upon rushing to that chapter (and fleeing asymptotic approximations!) it was gratifying to see many of the standard definitions, historical references, applications, computational algorithms and software (they cite my favorites, Mathematica and Maple). This was always one of the easier branches of math for me to follow and there is a natural affinity for the simpler and known quantity. Almost as understandable was the chapter on the Gamma function. Again, this was complemented by applications and computational sections and the mathematics was clear enough for most users of this class of functions.
As the 3j, 6j, 9j (angular momenta) and Airy functions chapters were no more dense than the above two, I must have started with the worst! I did however have a hard time navigating the Web site back to the original chapter listings. There is a tool on the left-hand side of the screen that allows the user to do this, but clicking on a title was not all that obvious to me, as it appeared mainly to be a header.
Never having used the original edition of this, and not being an engineer or physicist, it is hard to gauge to importance and usefulness of the site. However, the preliminary announcement did say that the 1964 edition had over a million copies in print and over 1,600 yearly citations in the research literature. It appears that many practitioners find this useful.
John Wass is a statistician based in Chicago, IL. He may be reached at editor@ScientificComputing.com.