Gradshteyn and Ryzhik

Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive

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

Overview

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

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

Pending this third German-English edition an English-only edition by Alan Jeffrey[nb 12] was published in 1965. Lacking a clear designation by itself it was variously known as first, third or fourth English edition, as it was based on the then-current fourth Russian edition. The formulas were photographically reproduced and the text translated. This still held true for the expanded fourth English edition in 1980, which added chapters 10 to 17.^[17]

Both of these editions saw multiple

The

In 1995, Alan Jeffrey published his Handbook of Mathematical Formulas and Integrals.[22] It was partially based on the fifth English edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and meant as an companion, but written to be more accessible for students and practitioners.^[22] It went through four editions up to 2008.^{[22][23][24][25]} The fourth edition also took advantage of changes incorporated into the seventh English edition of Gradshteyn and Ryzhik.^[25]

Inspired by a 1988 paper in which Ilan Vardi [de] proved several integrals in Gradshteyn and Ryzhik,^[26] Victor Hugo Moll with George Boros started a project to prove all integrals listed in Gradshteyn and Ryzhik and add additional commentary and references.^[27] In the foreword of the book Irresistible Integrals (2004), they wrote:^[28]

It took a short time to realize that this task was monumental.

Nevertheless, the efforts have meanwhile resulted in about 900 entries from Gradshteyn and Ryzhik discussed in a series of more than 30 articles

• LCCN ltf89006085. 400 pages.^[10][63]
• Рыжик, И. М. (1948). Таблицы интегралов, сумм, рядов и произведений (in Russian) (2 ed.). Moscow: Gosudarstvennoe Izdatel'stvo Tehniko-Teoretičeskoj Literatury (Государственное издательство технико-теоретической литературы) (GITTL / ГИТТЛ) (Tehteoretizdat / Техтеоретиздат). 400 pages.^[11]
• LCCN 52034158. 464 pages (+ errata inlet).^[63][64][65]
• LCCN 63027211. 1100 pages (+ 8 page errata inlet in later print runs).[108][109]^[14] Errata:^[66]
• LCCN 78876185. Dark brown fake-leather, 1108 pages.^{[nb 11]}
• ISBN 978-5-9775-0360-0. GR:11. l+1182 pages.^{[20][nb 11]}

• DNB-IDN 454242255, Lizenz-Nr. 206, 435/2/57. Retrieved 2016-02-21. Gray or green linen, xxiii+438 pages.^[15][16] Errata:^{[65][67][68][69][70][71][72]}
• Plenum Press, Inc., New York.) Green linen, xxiii+438 pages + 4 page errata inlet. Errata:^[70]

• DNB-IDN 551448512, 881086274, 881086282. Gray linen with gilded embossing by A. W. Schipow, 2 volumes, 677+3 & 504 pages.^[73][74]

• VIAF 309184374
  . Retrieved 2016-02-16. Light grayish cover, 464 pages.

• gilt titles, white dust jacket, xiv+1086 pages.^[1] Errata:^{[1][72][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]}
• ISBN 978-0-12-294760-5. GR:4,5,6,7. Retrieved 2016-02-21. xlvi+1160 pages.^[2][17] Errata:^{[2][17][93][94][95][96][97][98][99][100][101]}

• LCCN 96-801532 was prepared by Lightbinders, Inc. in July 1996.^{[102][103][4][5]}) Errata:^{[3][104][105][106][107][4][5][108]}

• ISBN 978-7-5062-6546-1 in April 2004.) Errata:^{[32][41][45][109][110][111][112][113]}

• ISBN 978-7-5062-8235-2 in May 2007.) Errata:^{[41][45][47][51][53][57][59][115]}
• ISBN 978-0-12-384933-5. GR:12. Retrieved 2016-02-21. xlvi+1133 pages.^[21] Errata:^{[116][30][117]}

• JPNO JP84018271
  . Retrieved 2016-04-06. xv+1085 pages.

• Prudnikov, Brychkov and Marichev
  (PBM)
• Bronshtein and Semendyayev (BS)
• Abramowitz and Stegun (AS)
• NIST Handbook of Mathematical Functions
  (DLMF)
• Jahnke and Emde
  (JE)
• Magnus and Oberhettinger
  (MO)

Notes