SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #12 --------------- OP-SF NET ---------------- November 15, 1996

From: Marvin Rosenblum
Subject: Review of Table of Integrals, Series, and Products, CD-ROM Version 1.0

(Editors' note: This review appeared earlier in Newsletter OP & SF, October 1996. This item was announced in Issue 3.1, Topic #14, revised in Issue 3.2, Topic #5.)

Table of Integrals, Series, and Products, CD-ROM Version 1.0, Edited by Alan Jeffrey, Academic Press, San Diego, California, USA, 1996, ISBN 0-12-294756-8

The venerable Gradshteyn and Ryzhik Table of Integrals, Series, and Products was originally planned by Ryzhik, who was later joined by Gradshteyn. The English translation was first published in 1965, and five editions of the volume followed in the next thirty years. In each edition there were corrections of errors and extensions of the material. Ryzhik died in World War II and Gradshteyn died during preparation for the fourth (1980) edition. The subsequent editions were and are edited by Alan Jeffrey.

The fifth edition of the book has been put on CD, which can be viewed from an IBM PC (or compatible) running Microsoft Windows 3.1, or 95, or NT, on a Mac, or on certain UNIX X-windows machines. Of course, there are minimum DRAM constraints, which only the foolhardy would ignore. I ran the CD using Windows 3.1. One can scan the book much as one can read the text of the printed fifth edition. But here one wants more, much more.

The major question is whether one can efficaciously search the CD so as to find integrals and/or integrands involving expressions that are of interest to the user. The manufacturer's guide asserts that the CD-ROM offers desktop access to the 20000 formulas for the integrals, sums, etc. The TeX source code for most formulae is obtained by clicking on a nearby icon. To perform the search one need study the TeX code for the expression that occupies your interest, activate the search panel, and fill in some variant of the studied TeX code. Wildcards are allowed.

The sad story here is that the search engine used preempts and prohibits use of the vital TeX characters

( , ) , < , > , =
It is very difficult to adapt the search program to do something other than find quotations of names of special functions. The TeX used on the CD is AMS-TeX, which is at this time not a usual dialect and thus provides a minor nuisance. I believe that the problem of designing a search mechanism to find TeX encoded mathematical expressions is interesting and challenging. I think it would be of interest to check with the experts working with the Latex3 project to see if they have suggestions on how it might be done.

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