4050 



Elliptic Functions, Division, etc. 



4050 



p dn u, squaring. Ferrers. N. M. Mess. Mth. 

 16 



= G *( U - ) ( u - b )( u ~ c ) ( u ~ 

 tion, new method. Kapteyn, W. Par. EC. 

 Norm. A. 9 (1892) 35-. 



, expression by logarithms. Dol- 



the 



bnia, I. A. Bll. Sc. Mth. 19 (1895) 76-; 

 Eec. Mth. (Moscou) 18 (1896) 108-. 

 6 [wW(z) - GJ], resolution into factors. Lacour, 

 E. Par. EC. Norm. A. 13 (1896) 415-. 



4050 Multiplication, division, 

 transformation of elliptic 

 functions; modular functions. 

 (See also 4440.) 



Algebra, transcendental, researches. Franchini, 

 P. Mod. S. It. Mm. 16 (1813) 223-; 17 

 (1815) 262-. 



Bisection. Igel,B. Crelle J. Mth. 119 (1898) 50-. 



Class-invariants. Mathews, G. B. [1890] L. 

 Mth. S. P. 21 (1891) 234-. 



numbers of binary quadratic forms, relations. 

 Hurwitz, A. Mth. A. 25 (1885) 157-. 



Congruence groups of 6th order. Fricke, E. 



Mth. A. 29 (1887) 97-. 

 Determinants formed from elliptic functions. 



Lerch, M. Prag Ceske Ak. Fr. Jos. Hz. 



(Tfida 2) 2 (1893) Art. 5, 5 pp. ; Fschr. Mth. 



(1893-94) 790. 



DIVISION. 



Abelian relations for. Engel, F. Leip. Mth. 



Ps. B. 36 (1884) 32-. 

 algebraic equations determining. Kronecker, L. 



Berl. Ak. Mb. (1875) 498-. 

 of argument. Emmanuel, D. [Bucarest S. 



Sc. Bll. 6 (1897)] 20-. 

 differential equation satisfied by roots of 



equations for. Migotti, A. Wien Ak. Sb. 



94 (1887) (Ab. 2) 748-. 

 of lemniscate. Liouville, J. C. E. 17 (1843) 



635-. 

 . Kohl, E. Wien Ak. Sb. 98 (1890) 



(Ab. 2o) 364-. 

 . Mathews, G. B. L. Mth. S. P. 27 



(1896) 367-. 



. Eipa, P. G. Mt. 38 (1900) 7-. 



, equation, irreducibility, etc. Eisenstein, 



G. Crelle J. 39 (1850) 160-, 224-. 

 , , separation into four factors. Schwering, 



K. Crelle J. Mth. 110 (1892) 42-; 112 



(1893) 37-. 



, equations, resolution. Schwering, K. 

 Crelle J. Mth. Ill (1893) 170-. 



periods. Brioschi, F. Mil. I. Lomb. Ed. 

 26 (1893) 727-; 27 (1894) 186-. 



, algebraic equations connected with. 

 Palmstrjm, A. Berg. Ms. Aarb. (1897) No. 4, 

 17pp. 



, resolvent of algebraic equation deter- 

 mining. Kiepert, L. Gott. Nr. (1885) 257-. 



of periods by 7, forms of equation determining. 

 Palmstrflm, A. Arch. Mth. Ntvd. 19 (1897) 

 No. 5, 17 pp. 



, Galois's resolvent. Halphen, 

 G. H. C. E. 108 (1889) 476-. 



, . Brioschi, F. C. E. 109 



(1889) 520-. 

 by 9. Burnside, W. Mess. Mth. 22 



(1893) 89-. 



theta-function. Klein, C. F. Mth. A. 17 

 (1880) 565-. 



Doubly periodic functions. Cayley, A. Liouv. 

 J. Mth. 10 (1845) 385- ; 19 (1854) 193-. 



, rational functions analogous to. 

 Vasil'ev, A. V. (xn) Kazan Un. Mm. [16] 

 (1880) (Pt. 2) 121-. 



Elliptic formulae of Jacobi, demonstration. 

 Somoff, J. [1851] St Pet. Ac. Sc. Bll. 10 

 (1852) 65-. 



functions. Klein, F. D. Nf. B. (*1877) 104. 

 , expansion, method. Schlomilch, O. 



Leip. B. (1853) 25-. 

 , in series. Broch, 0. J. [1863] Sk. 



Nf. F. 9 (1865) 146-. 



.theory. Krause,M. Mth. A. 12 (1877) 1-. 



, . Eausenberger, 0. Crelle J. Mth. 



93 (1882) 328- ; 94 (1883) 251-. 

 , . Weierstrass, C. T. W. Berl. Ak. 



Sb. (1882) 443- ; (1883) 193-, 265-, 1271-. 

 snnu. Cayley, A. Crelle J. 37 (1848) 



58. 

 of IK. Forsyth, A. E. Mess. Mth. 12 



(1883) 134-. 

 . Glaisher, J. W. L. Mess. Mth. 



20 (1891) 191-. 

 , etc. Burnside, W. Mess. Mth. 12 



(1883) 154-. 



integral, 1st kind, expansion, cases. Catalan, 

 E. C. As. Fr. C. E. 6 (1877) 214-. 



integrals, 1st and 2nd kinds, expansion in 

 recurring series. Farkas, J. C. E. 92 (1881) 

 181-. 



, , series. Hermite, C. 



A. Mt. 2 (1868-69) 97-. 

 , theory. Newman, F. W. B. S. P. 9 



(1857-59) 704-. 



normal curves and connected modular func- 

 tions. Klein, F. Leip. Mth. Ps. Ab. 13 

 (1887) 337-. 



Equation between 2 transcendental functions, 

 demonstration. Enneper, A. QJ. Mth. 1 

 (1857) 272-. 



Equations, 5th order, equations of icosahedron 

 in solution of. Klein, C. F. Mil. I. Lomb. 

 Ed. 10 (1877) 253-. 



Formulae for sn 9w. Sudo, 0. Tok. Coll. Sc. 

 J. 7 (1895) 283-. 



sn 10u, en lOw, dn 10w in terms of sn u. 



Sakai, E. Tok. Coll. Sc. J. 7 (1895) 285-. 



Functions with several periods not interchange- 

 able. Rausenberger, 0. Mth. A. 20 (1882) 



Gauss's pentagramma mirificum. Schlesinger, 

 L. Mth. Termt. Ets. 17 (1899) 526- ; Mth. 

 Nt. B. Ung. 17 (1901) 20-. 



325 



