zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Table of definite and infinite integrals. (English) Zbl 0556.44003
Physical Sciences Data, 13. Amsterdam - Oxford - New York: Elsevier Scientific Publishing Company. X, 457 p. \$ 106.50; Dfl. 250.00 (1983).

This table is a collection of integrals of elementary and special functions and it can be viewed as a useful addition to the well-known existing tables. The integrals presented here were compiled over many years from numerous scientific and technical journals and books or were obtained by the author himself. The result is a remarkable collection. There are slightly altered versions of well-known integrals. An example is on p.20, no. 24, which is obtained just by using the property ${K}_{\nu }\left(a\right)={K}_{-\nu }\left(a\right)$ for the Bessel function. (A further change $\nu \to \nu +1$ yields an error in no.25). An eye-catcher is no. 1 on p.48, which says that ${\int }_{0}^{\infty }tan\left(x+ia\right)dx=i\pi$ (Re $a>0\right)$, but the integral makes no sense to me.

Another one is no.22 on p.104, saying that ${\int }_{0}^{\infty }{x}^{n-}lnxsechxdx=0,$ with no restrictions on n (but I suppose $n=0,1,2,···\right)$. Is this correct? Of course it is not fair to consider just examples where the book is wrong. A random choice of, say, 100 items and check these ones would be a better treatment. However, although some of the results are easily verified, the bulk of the book is not, and verification of these 100 items would be very time-consuming. In the same manner, the book may be very useful for mathematicians, engineers and scientists, since it may save them lots of hours when they find the integrals they use in closed form. In any book of special functions errors will occur. I agree with Askey when he said that a formula in any such book may be a good start and always should be verified.

The presentation is clear and the table is well organized.

Reviewer: N.M.Temme

MSC:
 44A20 Integral transforms of special functions 00A22 Formularies 44-01 Textbooks (integral transforms) 33-01 Textbooks (special functions) 33-XX Special functions 26A09 Elementary functions of one real variable 26A42 Integrals of Riemann, Stieltjes and Lebesgue type (one real variable) 65A05 Tables (numerical analysis)