Customer Reviews

Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics)

5 star:		(15)
4 star:		(2)
3 star:		(2)
2 star:		(1)
1 star:		(0)

 

 

This book, originally published in 1964 by the National Bureau of Standards, is the result of a project started in 1954. It provides information on most of the functions then widely used in numerical computation in engineering and the physical sciences, including many formulas, and numerical tables of values for most of the functions.

In 2001 it has two drawbacks. First, because algorithms for computing numerical values of mathematically functions have improved dramatically over the 37 years since this work was published, you will not find suitable algorithms for computing values of the various functions discussed. To write a program for a computer or programmable calculator to produce values of any of these functions, you should use algorithms obtained from more modern works.

Second, and for much the same reason, you should not assume that all the numerical values given in all the tables are completely accurate; in 1964 calculations of some of these values with then-known algorithms pushed the state of the art to the limit. For example, in Table 7.3, "Complementary Error Function", two of the values attributed to a 1951 table by O. Emersleben are slightly incorrect in the last digit tabulated. This is not a criticism of this book, or of Emersleben; accurate calculation of values of the complementary error function for large arguments is tricky, and I have found similar errors in tables compiled more recently. However, good algorithms are now known, and should be used by anyone who desires reliable values.

These days I find this book still useful for refreshing my memory on various of the many formulas it contains, but for numerical values I prefer to rely on more recent sources, or on programs that derive values using the better algorithms known these days.

I probably would never have gotten my PhD without this book, and it is a stupendous classic. Nowdays, though, my first resort is always Maple or Mathematica, with their manifold capabilities. I still find it useful for trying to understand what those programs are doing by way of simplification (or, more commonly, not doing). Eventually Maple and Mathematica will figure out that they need to couple a powerful explanatory capability to their marvelous algorithms, and this book will become truly obsolete - but that date is not yet here as of 2004.

Four stars only because it has been partly overcome by history. 5 Plus for its historical importance.

A & S's Handbook of Mathematical Functions is an absolute must have for any lover of mathematics. The explanations are top rate. With the abilities of computers to tabulate numbers rapidly, the value of the tables is questionable. But the mathematical coverage is absolutely without equal. Any function you can think of, and some that you probably can't are covered in steamy, lurid detail. The paperback is such a great value that it makes me whinge to imagine that any lover of mathematics could possibly pass it by.

This book is a compendious of mathematical tables, formulas and graphics. It contains a very complete table of analytical integrals, differential equations and numerical series. Furthermore there are tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration and techniques for point interpolation and function approximation. There is a whole section for mathematical and physical constants as fractions and powers of Pi, e and prime numbers. Statistics are also discussed by presenting combinatorial analysis and probability functions. In its more than 1000 pages, almost all mathematical areas are treated. Every time you need same mathematical relation or information you will find it on this book. If you work with mathematical research or numerical computing you must have this book.

Certainly A&S is one of the very few books that have marked history for having become a standard reference text for functions. And with merit. I'd like to point out however the fact that there are certain drawbacks to its format: if You have to find out a specific property of a function You have to inspect every single bit of info You have at your disposal through the book; for example if You're looking for a property that is a particular case of a more general one You have first to identify the more general one, and this is certainly a difficult thing. Also another drawback is that functions with more than one parameter are not classified according to the value of the parameters themselves; You have to try to figure out the behaviour by yourself. Another bad thing is that not all the functions are graphed (example: Whittaker W and M). In any case, with its so large extent of covered topics, it is still the most valuable book of functions; for more specific or strange and particular subtopics or unusual properties You have to check the original texts where A&S took info from.

This book is a good overall summary of orthogonal functions. I did find it to be somewhat incomplete for prolate spheroidal wave functions, having to refer to the book from which they took their information. Overall, this book is a must-have for any physicist or mathematician. You can't beat the information per dollar density.

I have enjoyed using this book over quite some time. Its comprehensiveness promised to never let me down. It did keep the promise since the late seventies. Whenever I needed a clearer picture, perhaps a reason why a function did behave the way it did, I found the additional clarification here. Glad it exists.

The amount of material in this book still stuns me, as well as the
care that was taken in compiling it. Its influence is still felt in
that many people still use its nomenclature for special functions.

Many of the comments of the other reviewers are valid. However, one
should realize this book came from another era, one in which the
availability of digital computation resources weren't so prevalent or
cheap as they are today. When one had to evaluate an expression to
more significant figures than available on a slide rule, the
calculation had to be done with logarithms and tables. It was noxious
drudgery and error-prone to boot.

This book covers many, if not most, of the special functions a
technical person will be likely to encounter during his or her career.
The level of presentation is approximately at what one could expect of
a four year technical degree that has had exposure to the normal year
and a half of elementary calculus, a semester or two of advanced
calculus including differential equations, a semester of complex
variables, and possibly a numerical analysis course. However, the
book can still be used profitably even if you haven't had all that
background.

For $25 new or $5-10 used, it's hard to get this kind of information
density for such low cost. My copy is pretty beat up; it's marked at
$6.95 and I probably bought it in the late 1960's or early 1970's.

The NIST is working on a digital replacement of Abramowitz and Stegun.
Visit their website for an update.

It has been 40 years since Dover released this book. Its virtue has long been the extensive tables of somewhat obscure functions, like the hypergeometrics. In its time, many scientists, especially physicists, have used it as a well deserved standard reference. But times change. Nowadays it would be far more useful to readers if the tables were accessible in the form of a CD or DVD.

Though even then, this is problematic. When the book was published, most readers had no or little direct access to computers and, related to this, the ability to program them. So hardcopy tables were necessary. Whereas now, if you have a function, it might be more concise to generate a table. Indeed, Mathematica and Maple are, to some extent, competing products, with much greater functionality.

(First of all, excuse my english, is not my mother lenguage)

This book details math functions properties for the most and the less known functions. Starting with math and physical constants, only as an ilusion, cause the body kernel for this text is to take a function( transcendental, exponential, Gamma, Error, Legendre, Bessel, Jacobi......) and detail every property(formulas) and every useful numerical data(tables) you would know. But be careful, if you are serching for a complete list of more general formulas, may be you have to try in other texts( as i.e: Zwillinger's Standard Mathematical Tables and Formulae, edited by CRC Press), here you can't find matrices nor tensors, none about algebras, nothing on general analysis(calculus) but yes, you will find all the analytical properties for all the functions you use to use, and for those that only someone use... enjoy your book