The First 498 Bernoulli Numbers

Project GutenbergProject Gutenberg · United StatesDec 2019

1.3

Word count: 93K words
Chapters: 10

Summary

Project Gutenberg was the first provider of free electronic books, or eBooks. Michael Hart, founder of Project Gutenberg, invented eBooks in 1971 and his memory continues to inspire the creation of eBooks and related technologies today.The First 498 Bernoulli Numbers by Simon PlouffeAuthor: ,Language: English, Class: QA: Science: Mathematics, Release Date: Apr 1, 2001

Editor's review

This file, compiled by Simon Plouffe, presents the first 498 Bernoulli numbers and is a mathematical reference tool rather than a popular reader. Bernoulli numbers recur throughout number theory, combinatorics and series expansions, and this compilation gathers the first few hundred terms in one place for easy checking and programmatic verification. Its strength is high data density and a clear purpose, making it suitable as a lookup table for computation or derivation; its weakness is equally clear: it offers almost no derivations or background explanation and lacks the coherence of a textbook. It is chiefly a desk reference, consulted when writing code to verify algorithms, checking formulas, preparing exercises or doing small number theory investigations. For general readers it is more a raw data list than a book to read from cover to cover. Editorially it should be positioned as a mathematical reference, with a note that readers should use it alongside a textbook or computational tool to get value from it.

Who it's for

A good fit for

Students studying number theory or combinatorics who need to look up specific Bernoulli number values
Developers writing programs to verify Bernoulli number algorithms or run numerical experiments
Teachers preparing exercises or lecture notes who need to quickly check the first several values
Enthusiasts with some English reading ability who need to use mathematical data tables

Not a good fit for

Beginners hoping to systematically learn the definition, properties and derivations of Bernoulli numbers
General readers expecting a popular math book or historical narrative
Readers with no number theory background who just want to browse casually

Reading tips

Review the definition and generating function of Bernoulli numbers before consulting the table, so you are not just looking at numbers.
Use the file as a reference work, looking up specific terms as needed rather than reading it straight through.
Recompute the first several terms with your own program and compare them with the table to test your understanding.
When a term's purpose is unclear, return to the relevant textbook chapter to confirm its context and conventions.

About the publisher

Project Gutenberg United States · Founded in 1971

Project Gutenberg is a digital publishing project focused on public-domain ebooks. Its publishing direction centers on classic literary works whose copyright has expired, covering genres such as poetry, drama, fiction, and epic. Representative books include Lyrical Ballads by Wordsworth and Coleridge, Proust's Du côté de chez Swann, Shakespeare's Macbeth and The Complete Works of William Shakespeare, Homer's The Iliad, Dante's La Divina Comèdia: Purgatòri, Cervantes's The History of Don Quixote, Volume 2, and Grahame's The Wind in the Willows. Its author resources consist mainly of classic Western writers such as Wordsworth, Proust, Shakespeare, Homer, Dante, Cervantes, Grahame, and Tolstoy. Its publishing feature is the provision of freely accessible ebooks in EPUB and Kindle formats; it is not a traditional publisher, and publicly available information is limited.

FAQ

What does this material contain?

It lists the values of the first 498 Bernoulli numbers. It is a mathematical data table compiled by Simon Plouffe and released through Project Gutenberg. The file is mainly numerical and contains no systematic definitions or derivations.

What are Bernoulli numbers used for?

Bernoulli numbers appear in topics such as number theory, combinatorics and series expansions, for example in connection with power sum formulas and certain expansions. Their specific use must be understood through the relevant textbook chapters; a table of values alone will not teach it.

Can I use it to learn about Bernoulli numbers?

It is not suitable as an introductory text. It lacks definitions, properties and proofs, so beginners should read a textbook first and then use this table as an aid for checking values.

What should I watch out for when using this table?

Different sources may use different sign conventions for Bernoulli numbers. Before consulting it, confirm that the convention matches, so you do not introduce sign errors when plugging values directly into formulas.

Comments

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