4050 Elliptic Functions, Multiplication, Transformation 4050 



Moduli, Cauchy's theory, and two theorems. 



Piola, G., d Frisiani, P. Opusc. Mt. Fis. 2 



(1834) 49-, 173-, 301-. 

 of functions, principal. Cauchy, A. L. 



C. E. 20 (1845) 546-. 



Modulus of elliptic functions, and invariants 



of biquadratic binary forms, relations. 



Miiller, (Dr) F. Z. Mth. Ps. 18 (1873) 280-. 

 integrals, variation. Elevens de Haan, 



D. B. A. Ep. (1877) (Sect.) 23-. 



MULTIPLICATION. 



Laguerre, E. [1877] Par. S. Mth. Bll. 6 (1878) 



68-. 

 Frobenius, G., & Stickelberger, L. [1879] 



Crelle J. Mth. 88 (1880) 146-. 

 Halphen, G. H. C. E. 88 (1879) 414-. 

 Novarese, E. Tor. Ac. Sc. At. 17 (1881) 723-. 

 Kronecker, L. Berl. Ak. Sb. (1883) 717-, 



949-. 



Fujisawa, E. Tok. Coll. Sc. J. 6 (1894) 151-. Multiplicator equations. Klein, C. F. [1878] 

 and addition, geometric. Trudi, N. Nap. Ed. Mth. A. 15 (1879) 86-. 



2 (1853) 66-. f higher degree. Biedermann, P. Leip. 



of argument, two partial differential equations Mth. Ps. B. 37 (1885) 201-. 



relating to. Halphen, G. H. C. E. 88 Biedermann, P. Arch. Mth. 



(1879) 698-. Ps. 5 (1887) 1-. 



complex. Kronecker, L. Berl. Mb. (1857) Octavic equation having group of modular 

 455-; (1862) 363-; Par. EC. Norm. A. 3 transformation, 7th order. Brioschi, F. Mil. 



I. Lomb. Ed. 1 (1868) 68-. 

 Poncelet's polygons. Lelieuvre, M. Ens. Mth. 



2 (1900) 410-. 



Substitution, double, in elliptic functions, 

 principle. Eaabe, J. L. Crelle J. 15 (1836) 



formulas. Cayley, A. Crelle J. 39 (1850) 



16-; 41 (1851) 85-. 



. Hoffmann, H. Crelle J. 48 (1854) 332-. 

 . Brioschi, F. C. E. 59 (1864) 769-. 

 , deduction of infinite double products from. 



Mittag-Leffler, G. Stockh. Ofv. 33 (1876) 



No. 6, 17-. 

 for integers, in connection with Poncelet's 



problem, etc. Simon, M. Crelle J. Mth. 81 



(1876) 301-. 

 of 4 theta functions, formula for. Smith, 



H. J. S. L. Mth. S. P. 10 (1878-79) 91-. 

 and transformation. Sanio, J. T. Crelle J. 14 



(1835) 1-. 

 , new formulae in. Brioschi, F. A. Mt. 



23 (1895) 73-. 

 of en u, algebraic derivation. Eunge, C. 



Crelle J. Mth. 94 (1883) 349-. 



(1866) 295-. 

 . Greenhill, A. G. [1882] Camb. Ph. S. 



P. 4 (1883) 271-. 

 . Pick, G. [1885] Mth. A. 25 (1885) 433- ; 



26 (1886) 219-. 

 . Stuart, G. H. QJ. Mth. 20 (1885) 18-, 



221-. 

 . Greenhill, A. G. Camb. Ph. S. P. 5 



(1886) 4- ; QJ. Mth. 22 (1887) 119-, 174. 

 . Sylow, . Liouv. J. Mth. 3 (1887) 109-. 

 . Weber, H. Mth. A. 33 (1889) 390- . 

 . Kiepert, L. Mth. A. 39 (1891) 145-. 

 , geometric application. Kiepert, L. [1871] 



Crelle J. 74 (1872) 305-. 

 , with imaginary modulus. Cayley, A. L. 



Mth. S. P. 19 (1889) 300-. 

 , moduli. Greenhill, A, G. [1888] L. Mth. 



S. P. 19 (1889) 301-. 

 , . Mathews, G. B. [1889] L. Mth. S. P. 



21 (1891) 215-. 

 , , table. Greenhill, A. G. [1890] L. Mth. 



S. P. 21 (1891) 403-. 

 , and quadratic forms. Franel, J. Mth. A. 



48 (1897) 595-. 

 , of theta functions. Scheibner, W. Leip. 



Mth. Ps. B. 40 (1888) 154-. 

 , by V/-23. Brioschi, F. A. Mt. 24 (1896) 



335-. 

 , especially. Halphen, G. H. Liouv. 



J. Mth. 5 (1889) 5-. 

 and division of elliptic integrals. Kilpper, C. 



Schlomileh Z. 7 (1862) 239-. 

 of doubly periodic functions of 2nd kind. 



Krause, M. Leip. Mth. Ps. B. 42 (1890) 



24-. 

 of elliptic functions of first kind. Baehr, 



G. F. W. Grunert Arch. 36 (1861) 125-. 

 formula, Jacobi's. Brioschi, F. Mil. I. Lomb. 



Ed. 1 (1864) 344-. 



191 



groups for roots of A; 2 (u). Fricke, E. Mth. 

 A. 28 (1887) 99-. 



, linear, finite groups, in theory of elliptic 



transcendents. Hurwitz, A. Mth. A. 27 



(1886) 183-. 

 , , for reduction of elliptic functions of 1st 



kind. Tortolini, B. Tortolini A. 1 (1858) 



57-. 

 Theorem of Legendre, extension. Malet, J. C. 



A. Mt. 11 (1882-83) 246-, 312-. 

 Theta-characteristics, groups. Frobenius, G. 



Crelle J. Mth. 96 (1884) 81-. 

 , theory. Ameseder, A. Wien Ak. Sb. 



93 (1886) (Ab. 2) 618-. 



functions with complex characteristics. 

 Craig, T. Am. J. Mth. 6 (1884) 337-. 



TEANSFOEMATION. 



Cayley, A. Ph. Mg. 25 (1844) 352-; 27 



(1845) 424-. 



Brioschi, F. Tortolini A. 8 (1857) 70-, 125-. 

 Casorati, F. Tortolini A. 8 (1857) 209-. 

 Brioschi, F. Tortolini A. 1 (1858) 175-. 

 Bjerknes, C. A. Christiania F. (1860) 152-. 

 Hertz, K. [1869] (xn) Eec. Mth. 



(1869-70) (Ft. 1) 139-. 



A. 



(xn) Eec. Mth. (Moscou) 4 

 139-. 

 [1873] Phil. Trans. 164 (1874) 



Cayley, 



397 

 Clifford, W. K. [1875-76] L. Mth. S. P. 7 



(1876) 29-, 225-. 

 Laguerre, E. [1876-77] C. E. 82 (1876) 1257- ; 



Par. S. Mth. Bll. 6 (1878) 72-. 



327 



