Gradshteyn and Ryzhik

Table of Integrals, Series, and Products

Gradshteyn and Ryzhik, seventh English edition, 2007
Author	Ryzhik, Gradshteyn, Geronimus, Tseytlin et al.
Country	Russia
Language	Russian, German, Polish, English, Japanese, Chinese
Genre	Math
Publisher	Academic Press
Publication date	1943, 2015

Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik. Its full title today is Table of Integrals, Series, and Products.

Since its first publication in 1943, it was considerably expanded and it soon became a "classic" and highly regarded reference for mathematicians, scientists and engineers. After the deaths of the original authors, the work was maintained and further expanded by other editors.

At some stage a German and English dual-language translation became available, followed by Polish, English-only and Japanese versions. After several further editions, the Russian and German-English versions went out of print and have not been updated after the fall of the Iron Curtain, but the English version is still being actively maintained and refined by new editors, and it has recently been retranslated back into Russian as well.

One of the valuable characteristics of Gradshteyn and Ryzhik compared to similar compilations is that most listed integrals are referenced. The literature list contains 92 main entries and 140 additional entries (in the eighth English edition). The integrals are classified by numbers, which haven't changed from the fourth Russian up to the seventh English edition (the numbering in older editions as well as in the eighth English edition is not fully compatible). The book does not only contain the integrals, but also lists additional properties and related special functions. It also includes tables for integral transforms. Another advantage of Gradshteyn and Ryzhik compared to computer algebra systems is the fact that all special functions and constants used in the evaluation of the integrals are listed in a registry as well, thereby allowing reverse lookup of integrals based on special functions or constants.

On the downsides, Gradshteyn and Ryzhik has become known to contain a relatively high number of typographical errors even in newer editions, which has repeatedly led to the publication of extensive errata lists. Earlier English editions were also criticized for their poor translation of mathematical terms and mediocre print quality.

The work was originally compiled by the Russian mathematicians Iosif Moiseevich Ryzhik (Russian: Иосиф Моисеевич Рыжик, German: Jossif Moissejewitsch Ryschik) and Izrail Solomonovich Gradshteyn (Russian: Израиль Соломонович Градштейн, German: Israil Solomonowitsch Gradstein). While some contents were original, significant portions were collected from other previously existing integral tables like David Bierens de Haan's Nouvelles tables d'intégrales définies (1867),Václav Jan Láska's Sammlung von Formeln der reinen und angewandten Mathematik (1888-1894) or Edwin Plimpton Adams' and Richard Lionel Hippisley's Smithsonian Mathematical Formulae and Tables of Elliptic Functions (1922).