ELLIPTIC FUNCTIONS

In the higher mathematics the term Elliptic Function is used to designate any integral comprised in the formula / — ^ —, in which P is a rational function of j, and R is a radical of the form v/(<»+/3 x+y x2+ J x^^t x"*); «, yg, y, h, i, being constant quantities. Such integrals are called elliptic functions because they either contain, or are closely connected with expre ions for the arc of an ellipse. The principal works on the subject are the following: Exercises de Calcul Integral, 3 vols. 4to. 1811'; and Theorie des Fonctions Ellipttques, 3"vols. 4to. 1825—1828, by Legendre; (Euvres de N. H. Abel, 2 vols. 4to. 1839; and Jacobi's Fundament a Nova Theories Functionum Elliptic arum, 4to. 1829. [s. 1382]