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Rating: 
Summary: Improved my insight and understanding each time used
Review: 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.
Rating: 
Summary: Once Great
Review: 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.
Rating:
Summary: Once Great
Review: 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.
Rating:
Summary: un grimoire mathématique unique en son genre!
Review: Physicien, Handbook of mathematical functions est pratiquement mon livre de chevet. je le consulte bien plus qu' aucun autre document de physique, même plus que les revues spécialisées dans mon domaîne! L' un des apports les plus importants de ce livre dans mon cheminement est qu' il m' a permi de concevoir des algorithmes numériques pour presque toutes les fonctions spéciales dont j' avais besoin pendant mes recherches, notamment les fonctions Beta et Polygamma d' arguments complexes qui interviennent très fréquemment dans les calculs de susceptibilités électroniques dans les problèmes de supraconductivité. Bien des collègues et amis, travaillant notamment en chimie-physique et même en biologie, reconnaissent que ce livre est un tout pour qui a besoin des mathématiques dans ses recherches. Dire que sa mouture de base fut conçue en 1964!
Rating:
Summary: The most important handbook I ever seen
Review: 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.
Rating:
Summary: A Must Have but with drawbacks
Review: 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.
Rating: 
Summary: Excellent, but with limitations
Review: 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.
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