''Fundamenta nova theoriae functionum ellipticarum'' (New Foundations of the Theory of Elliptic Functions) is a book on

Jacobi elliptic functions In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While tri ...

Carl Gustav Jacob Jacobi Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasiona ...

.Given in Latin style as ''Carolo Gustavo Iacobo Iacobi'' in the book 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

and the

Jacobi triple product identity In mathematics, the Jacobi triple product is the mathematical identity: :\prod_^\infty \left( 1 - x^\right) \left( 1 + x^ y^2\right) \left( 1 +\frac\right) = \sum_^\infty x^ y^, for complex numbers ''x'' and ''y'', with , ''x'', < 1 and ''y' ...

References

;Citations ;General * * * *{{Citation , last1=Jacobi , first1=C. G. J. , title=Gesammelte Werke , origyear=1881 , url=http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_JACOBI__1 , publisher=Chelsea Publishing Co. , location=New York , edition=2nd , series=Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften , mr=0260557 , year=1969 , volume=I–VIII , access-date=2012-10-14 , archive-url=https://web.archive.org/web/20130513144451/http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_JACOBI__1 , archive-date=2013-05-13 , url-status=dead Mathematics books History of mathematics Elliptic functions 19th-century Latin books