Customer Reviews

Table of Integrals, Series, and Products, Sixth Edition

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I bought Gradshteyn & Ryzhik because I had to write an answer to some homework problem in some physics class that I took. The problem had contorted itself into a perverse elliptic integral and its recovery was beyond my means, so I went to the bookstore, looked for something fat and Soviet, and found this gem. I forked over the cash for it, figuring that it was a long-term investment.

I took it home and dutifully plagiarized some of its lines to satisfy my physics professor. For the next few months, that was the mode in which I used this book: read physics problem, translate into elliptic or hypergeometric beast, look up answer in G&R, cover up my tracks, get 9 or 10 points on the problem. Occasionally, I would own up to having looked something up.

The book served its purpose well. Subsequently, I studied some integrals of the spinning top that were more or less right out of Nikiforov's book on special functions (another excellent source for those of you that would like to "earn" a PhD), and G&R stood well by its side. Indeed, I discovered how much fun it was to look up an integral whose complicated solution had been derived elsewhere, and then to look for patterns by analyzing the immediate neighbors of the given integral on the preceding and subsequent lines in G&R.

After I was done with answering questions from physics professors, the book sat on the shelf taking up more room than several of its neighbors put together. Nonetheless, its binding was good, its typesetting clear, and its terse and copious stream of forbidding integral forms was pleasing to the eye.

Some time passed, and one day I asked myself just what would motivate anybody to write such a large collection, so I started rummaging through its pages looking for a pattern. I realized that its organization was excellent (which would explain why I was able to find the answers for my homework), and I also found some sections that were just plain fun. The very beginning lists some sums of infinite series that can be derived during lunch or while waiting for a friend at a cafe (e.g. sum of k^3 = [1/2(n)(n+1)]^2 ). Then one can read about numbers and functions named after Euler, Jacobi, Bernoulli, Catalan... each line, more or less, is cross-referenced, so after you have given up trying to derive that darned product representation of the gamma function, you can go to the book in the library and see how Whittaker did it.

After about 15 years of owning this book, I am nowhere near done with it. If you like math, and you want insurance against being bored, this book just might do the trick. As a bonus, it puts cute matrix stuff in the back (e.g. the "circulant") which one can read when desiring a break from the integrals. I know the book seems expensive, but think of if as spending about two bucks a year on it.

I see that one can now obtain a CDRom version of G&R. An intriguing option, specially because it outputs in TeX; but really, how can anyone resist the large, stubby charm of its paper version?

G&R can help you to deal with members of the opposite sex. I once used it to scare away a girlfriend that was becoming much too annoying, by pretending to be thickly engrossed in the process of memorizing every single integral in the "special functions" chapters. As for my mother, she was particularly proud of me when I showed her that I could actually understand "randomly selected" pages from this book (I don't suppose that I am giving anything away by remarking that books open naturally on sections that have been previously examined).

For those of you that are concerned about home security, G&R is also a weapon. Some people surround themselves with baseball bats or, if they are particularly reckless, a handgun or two... I prefer to keep a fully-loaded G&R by my pillow, which I can hurl at any prowler at a moment's notice. Its shape is surprisingly well adjusted to the hand for the purposes of hurling, and if the covers are bound by a rubber band, the book maintains its shape quite stably as it sails across the room. Sell your Smith & Wesson and buy yourself a Gradshteyn & Ryzhik. You won't regret it.

Before it was much use, I had to read the section as to how the book is organized. As the other reviewers state the integrals are comprehensive and as far as I have used correct. The integrals are very useful, but this book includes many other features that I have found helpful as a graduate student. The sections on Hermite and Legendre polynomials are especially helpful for students of Electricity and Magnetism, Quantum Mechanics, and Mathematical physics (you won't have to hunt in several books to find what you need). The included identities for hyperbolic and trig functions are very helpful simplifying homework answers, mostly because of their comprehensive nature. This book is great because it seems to have everything and most people will not need to buy another table. The binding is good also, so it should last many years with normal care. This is a very good investment.

Let's keep this short and sweet. The book is probably THE best in what it claims to be, i.e. a compendium of mainly integrals, but all sorts of interesting stuff also manages to find its way in. Why some former reviewers exhaust their artillery in complaining about the CD is beyond me. This is a reference BOOK an as such unsurpassed. Buy it for sheer pleasure if for nothing else. While you're at it, you might want to take a look at Handbook of Mathematics by I. N. Bronshtein et al. which I ordered from Amazon in Germany a moment ago. That one also comes with a CD and I'm getting curious about how it will turn out to be. But Gradshteyn and Ryzhik - the BOOK - are a must.

This is the best table of integrals available anywhere. Completely comprehensive and well organzied, it is a great companion to "Handbook of Mathematical Functions" by Abramowitz and Stegun.

My copy of this book is the 4th edition, 1965. I still vividly
remember going to a bookstore in Berkeley, CA in 1971 and buying this
book for $10 (I also bought the "Feynman Lectures in Physics" on this
trip for $7.45 per volume). I also remember eating lunch at an
outdoor restaurant in Berkeley and having a fantastic view of the San
Francisco Bay Area, as it was an absolutely clear day. As a piece of
useless trivia, I had a liverwurst sandwich on a dark pumpernickel;
this is the first time I ever had liverwurst and fell in love with it!

This book is compendium of mostly integrals. What made it stand out
back then was its organization, making it relatively easy to look
up a particular integral. Most of the formulas come with a reference
to where the formula came from, should one desire to research things
a bit more. While it's not a panacea for dealing with all integrals,
you're likely to find something in here to aid in attacking most
problems.

Before using any of these integrals in an important problem, I'd
recommend you verify the formula first. Fortunately, this isn't
hard to do numerically with modern scripting languages like python,
accompanied by something like scipy, or a computer algebra system
such as Mathematica or Maple.

Perhaps the most interesting part of this book is missing. For a comprehensive listing of integrals, there is no better book than this. Remarkably easy to find a desired integral, if the book covers it at all.

Yet what could be equally informative is a description of how some of the more intricate integrals were derived. Was it just pure ingenuity on the part of the original authors? Surely some of this is true. But did they also have methods that let them systematically find those results? For some readers, knowing these methods might let them derive other results not in the text. Then again, you might usefully assign yourself the task of ascertaining what those methods might have been, working backwards from the published results.

By the way, others have commented on the out of date CD. Good point. Perhaps what has stymied the publisher from updating the CD is the sheer amount of formatting, in TeX or any other markup language. Very labour intensive. Far harder than just scanning in normal text that is in one font, using optical character recognition, and then outputting it in a new font. Still, given what the publisher is asking for the 6th edition hardcopy (more than $100!), surely it could spend the money to reformat.

I have found the book to be very useful and informative.