Fundamenta nova theoriae functionum ellipticarum
One of the most exciting moments of my life was when, after computing several of these series, I went down to our mathematical library and found some of them in Jacobi's "Fundamenta nova theoriae..."[3], with the same coefficients down to the last decimal digit!
Conway (1980, p.171) describing the discovery of monstrous moonshine.
In mathematics, Fundamenta nova theoriae functionum ellipticarum[1] (new foundations of the theory of elliptic functions) is a book on Jacobi elliptic functions by Carl Gustav Jacob Jacobi.[2] The book was first published in 1829, and has been reprinted in volume 1 of his collected works and on several later occasions. The book introduces Jacobi elliptic functions and the Jacobi triple product identity.
References
- Citations
- ^ Fundamenta nova theoriae functionum ellipticarum. By Carl Gustav Jacob Jacobi. Sumtibus fratrum, 1829.
- ^ Given in Latin style as Carolo Gustavo Iacobo Iacobi in the book
- General
- Conway, John Horton (1980), "Monsters and moonshine", The Mathematical Intelligencer, 2 (4): 165–171, doi:10.1007/BF03028594, ISSN 0343-6993, MR 0600222
- Cooke, Roger (2005), "Chapter 31 C. F. G. Jacobi, book on elliptic functions", in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640–1940, Elsevier B. V., Amsterdam, pp. 412–430, ISBN 978-0-444-50871-3, MR 2169816
- Jacobi, C. G. J. (1829), Fundamenta nova theoriae functionum ellipticarum (in Latin), Königsberg: Borntraeger, ISBN 978-1-108-05200-9, Reprinted by Cambridge University Press 2012
{{citation}}: ISBN / Date incompatibility (help) - Jacobi, C. G. J. (1969) [1881], Gesammelte Werke, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften, vol. I–VIII (2nd ed.), New York: Chelsea Publishing Co., MR 0260557