No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 15 September 2014
As is well known, the usual form of the Addition-Theorem for Elliptic Functions of several arguments expresses these functions as the quotient of two determinants. When two or more arguments become equal, both numerator and denominator of this quotient vanish, and in seeking to remove the common vanishing factor, Cayley, in his paper “Note sur l'addition des fonctions elliptiques,” in connection with the cases of three and four arguments, brought to light some identities connecting certain alternants. Cayley gave these identities without proof, saying, “Je n'ai pas encore trouvé la loi générale de ces équations.”
page 240 note * Crelle's Jour., xli. pp. 57–65; or, Collected Math. Papers, i. pp. 540–549.
page 240 note † Trans. Boy. Soc. Edin., vol. xl. part i. (No. 9).
page 243 note * Clebsch, Cf., Geometrie, i.; Fünfte Abtheilung, vii. Laeroix, , Calcul diff. et int., 6th ed., Paris, 1862, p. 68.Google Scholar Bertrand, Calcul int., pp. 578–583. Koenigsberger, Elliptische Functional, ii. pp. 1–17. Story, American Jour. Math., vol. vii. No. 4. Abel, “Recherches sur les fonctions elliptiques,” Journal für Mathematik, Bd. ii. Kronecker, , Sitzungsberichte Der Akademie, Berlin, 1883, S. 717–729; 1883, S. 9497–956; 1886, S. 701–780.Google Scholar