Gradshteyn-Ryzhik

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Gradshteyn-Ryzhik. 5th edition 1994
Gradshteyn-Ryzhik. 7th edition 2007

The Gradshteyn-Ryzhik ( GR ) is an extensive integral table . The German edition appeared under the title Summen-, Produkt- und Integral-Tafeln , the English edition as Table of Integrals, Series, and Products.

content

The special and valuable thing about Gradshteyn-Ryzhik is that in all editions almost every integral is proven by a source. The bibliography for this includes 92 and 140 additional entries (8th edition). The integrals are classified according to numbers that have remained unchanged from the 4th Russian edition 1962 to the 7th English edition (there is no full compatibility with earlier editions and the 8th English edition). The work not only lists the integrals themselves, but also properties and developments of the special functions that occur . At the end there are tables for the integral transformation . With Gradshteyn-Ryzhik, a decisive advantage over computer algebra systems becomes clear (despite the still very high number of printing errors): there is a register for all special functions and constants that occur in the evaluation of all integrals. Thus the opposite question can also be answered: by which integrals is a given special function or constant represented.

history

The work was founded by the Soviet mathematicians Israil Solomonowitsch Gradstein (Израиль Соломонович Градштейн) and Jossif Moissejewitsch Ryschik (Иосиф Моисеевич Рыжик). The first two editions in 1943 and 1948 were edited by Ryschik. After his death, the third edition was edited in 1951 by Gradstein, who planned a considerable expansion in the fourth edition, but whose death prevented a realization. Juri Weneaminowitsch Geronimus (Юрий Венеаминович Геронимус) and M. Ju. Zeitlin then worked on the fourth and fifth editions.

Based on the third Russian edition (1951), the first German-English edition was published by Deutscher Verlag der Wissenschaften (East Berlin) in 1957 with a German translation by Christa and Lothar Berg and an English translation by Martin Strauss (438 pages). Karl Prachar writes in the Zentralblatt MATH : “The very extensive tables were only translated from Russian into German and English.” A second edition as an unchanged reprint follows in 1963 (with a four-page correction supplement by Eldon Hansen ). In 1981 the third German-English edition was edited by Ludwig Boll using the 1963 edition and was now based on the fifth Russian edition (1971).

In 1964 a Polish translation of the third Russian edition by Roman Malesiński was published.

From 1965 onwards, Alan Jeffrey edited an expanded English translation of the fourth Russian edition (1962), later called the third edition. The last edition with the assistance of Jeffrey was published in 2007 as the seventh English edition and comprised approx. 1200 pages. From the sixth English edition (2000), Daniel Zwillinger also worked on the publication, who after Jeffrey's death continued the project together with Victor Hugo Moll in the current eighth English edition from 2014.

Comparable projects and follow-up projects

Anatoli Platonowitsch Prudnikow , Yuri Alexandrowitsch Brytschkow and Oleg Igorewitsch Maritschew are supervising a comparable project with their five-volume work Integrals and Series (Russian original edition Moscow, 1981–1986; new edition Moscow, 2003). Here, too, the integrals are classified according to numbers, but there are no references to literature and the register is very poor.

Victor Hugo Moll started as a gigantic project to prove all integral evaluations from Gradshteyn-Ryzhik and to enrich them with further considerations and sources. In the foreword of Irresistible Integrals (2004) he writes :

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

In the meantime, the result is already very remarkable and was reflected in his two-volume book series Special Integrals of Gradshteyn and Ryzhik: The Proofs (2014-2015).

pads

Russian editions

  • 1943 1st Russian edition, 400 pages; Ryschik, Zbl 0060.12305
  • 1948 2nd Russian edition, 400 pages; Ryschik, Zbl 0034.07001
  • 1951 3rd Russian edition, 464 pages; Ryschik and Gradstein, Zbl 0044.13303
  • 1962 4th Russian edition, 1100 p .; J. Geronimus and M. Zeitlin, Zbl 0103.03801
  • 1971 5th Russian edition, 1108 p .; J. Geronimus and M. Zeitlin
  • 2011 7th Russian edition, 1232 p .; Alan Jeffrey, Daniel Zwillinger, Vasily Vasilyevich Maximov (Василий Васильевич Максимов). ISBN 978-5-9775-0360-0

German editions

Polish edition

  • 1964 1st Polish edition, 464 pages; Roman Malesiński

English editions

Japanese edition

The third, two-volume German-English edition from 1981 (MIR Moscow publishing house, gray linen cover with gold embossing by AW Schipow) is particularly well known.

Individual evidence

  1. ↑ Zbl 0080.33703 (1st German-English edition 1957)
  2. ^ Table of Integrals, Series, and Products. Academic Press, 2007, ISBN 978-0-12-373637-6
  3. ^ Table of Integrals, Series, and Products. Academic Press, 2014, ISBN 0-12-384933-0
  4. ↑ George Boros, Victor Hugo Moll: Irresistible Integrals. Symbolics, Analysis and Experiments in the Evaluation of Integrals . Cambridge University Press, 2004, ISBN 0521796369 (This edition contains a large number of typographical errors.)
  5. ^ Victor Hugo Moll: Special Integrals of Gradshteyn and Ryzhik: the Proofs. Volume 1 ( Series: Monographs and Research Notes in Mathematics ). Chapman and Hall / CRC, 2014, ISBN 978-1-4822-5651-2 .
  6. ^ Victor Hugo Moll: Special Integrals of Gradshteyn and Ryzhik: the Proofs. Volume 2 ( Series: Monographs and Research Notes in Mathematics ). Chapman and Hall / CRC, 2015, ISBN 978-1-4822-5653-6 .

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