4060 Abelian Integrals 



Hyperelliptic surfaces, general theory. Hum- 

 bert, G. Liouv. J. Mth. 9 (1893) 29-, 361-. 



system of general form, explicit expression 

 of algebraic integral. Salvert, F. de. C. E. 

 116 (1893) 243-. 



systems of barriers. Thompson, H. D. Am. 

 J. Mth. 15 (1893) 91-. 



Integral equations, new, of Jacobi's system of 



differential equations. Richelot, F. J. 



Crelle J. 25 (1843) 97-. 

 Integrals, class, involving roots of polynomials. 



Minding, E. F. A. Crelle J. 10 (1833) 195-, 



292. 



of solutions of 2nd order of differential 

 equations, with 3 singular points. Kejainski, 

 S. Krk. Ak. (Mt.-Prz.) Ez. 17 (1900) 112- ; 

 Crc. Ac. Sc. Bll. (1899) 67-. 



Inversion problem. Jacobi, C. G. J. Crelle 



J. 32 (1846) 176-. 

 , Jacobi's. Goursat, E. Bll. Sc. Mth. 19 



(1895) 24-. 



, , generalisation. Lindemann, C. L. F. 



[1878] Freiburg B. 7 (1880) 273-. 



, __, solution. Stahl, H. Crelle J. Mth. 



89 (1880) 170- ; 111 (1893) 98-. 



Kleinian prime forms and automorphic func- 

 tions. Ritter, E, Mth. A. 44 (1894) 261-. 



Minding' s integral \dx(\.-a?)~, reduction to 



elliptic integral of 1st kind. Richelot, F. J. 



Crelle J. 9 (1832} 407-. 

 Multiply-tangential curves to algebraic curves. 



Weiss, W. Mh. Mth. Ps. 7 (1896) 370-. 

 Number of periods of uniform function. Astor, 



A. N. A. Mth. 15 (1896) 227-. 

 functions. MUhll, K. von der. 



Basel Vh. 9 (1893) 78-. 

 Parameters, representation of algebraic curves 



by. Enriques, F. Palermo Cir. Mt. Ed. 10 



(1896) 30-. 



Quadruple theta functions, relations satisfied by. 



Craig, T. Am. J. Mth. 6 (1884) 205-. 

 Eepresentation of function in Eiemann surface, 



with variable multipliers of periodicity. 



Suchar, P. I. [Bucarest S. Sc. Bll. 7 (1898)] 



143-. 

 Eiemann's integrals of 1st species, canonical 



form. Christoffel, E. B. A. Mt. 9 (1878- 



79) 240-. 

 Theorem in geometry of n dimensions. Segre, 



C. Mth. A. 30 (1887) 308. 

 Theorems. Abel,N.H. N. A. Mth. 4 (1845) 536-. 

 Theta functions, Jacobian, partial values, and 



Gauss's posthumous papers. Goring, W. 



Mth. A. 7 (1874) 310-. 

 with ^-series, characteristics formed of 



thirds of integers. Braunmilhl, A. von. 



Erlang. Ps. Md. S. Sb. 18 (1886) 37-; 



Munch. Ak. Ab. 16 (1888) 325-; Mth. A. 32 



(1888) 513-. 



, nths of integers. 



Braunmiihl, A. von. Mth. A. 37 (1890) 61-. 



, theorems. Bock, W. Hamb. Mth. Gs. 



Mt. 2 (1890) (Festschr., Tl. 2) 74-. 

 Transcendental functions. Abel, N. H. (n 



Adds.) Norske Vd. Skr. 2 (1824-27) (2d Heft) 



Periodic Functions 4070 



Transcendental f unctionswith algebraic differen- 

 tials, summation. Jilrgensen, C. Kiob. Dn. 

 Vd. Selsk. Afh. 8 (1841) 17-; Crelle J, 19 

 (1839) 113-. 



Transcendents, of which hyperelliptic functions 

 are special case. Laguerre, E. C. E. 84 

 (1877) 643-. 



Univocal correspondences on elliptic curves 

 (application of Abelian integrals). Patrassi, 

 P. G. Mt. 34 (1896) 195-. 



hyperelliptic curves. Kantor, S. Pa- 

 lermo Cir. Mt. Ed. 9 (1895) 65-. 



p ~, integration. Abel, N. H. Crelle J. 1 



(1826) 185-. 



, Abel's theorems, demonstration. Dolb- 

 nia, I. P. Kazan S. Nt. (Ps.- Mth.) P. 6 

 (1888) 307- ; Fschr. Mth. (1888) 486. 



U/l + cur 3 . dx. Minding, E. F. A. Crelle J. 9 

 (1832) 295-. 

 , integration, E, F, \(/, being rational in- 



tegral functions of same variable. Mainardi, 

 G. Yen. Mm. I. 2 (1845) 401-. 

 Al(x), Al 1 (x), Al% (x), expansion in powers of 

 modulus. Andre, D. Liouv. J. Mth. 5 

 (1879) 131-. 



here fx> y=0 and <f>{x> =0> 



3 (x, y) 



and theorem of Jacobi. Forsyth, A. R. QJ. 



Mth. 18 (1882) 313-. 



fG(x) dx ^ Guichardt Cm c B> 104 ( 1887 ) 

 J Kj R (x) 



1494-. 



4070 Periodic functions of several 

 variables ; general theta func- 

 tions. 



Abelian functions. Poincare, H. C. E. 124 



(1897) 1407 -. 



, addition. Salvert, (le vicomte) de. 

 Brux. S. Sc. A. 17 (1893) (Pt. 1) 70-; 18 

 (1894) (Pt. 2) 41-. 



-- , generalisation. Picard, E. C. E. 98 



(1884) 665-. 

 -- , integration by. PoincarS, H. C. E. 92 



(1881) 913-. 

 -- , 1st order, modular equations for trans- 



formation of 3rd degree. Konigsberger, . 



[1868] Mth. A. 1 (1869) 161-. 

 -- with 4 periods. Roberts, M. [1870] A. 



Mt. 4 (1870-71) 95-. 

 -- and quadratic forms of n differentials. 



Lipschitz,R. [1871] Crelle J. 74 (1872) 150-. 



, singular. Humbert, G. C. E. 126 



(1898) 508-. 



, transformation. Humbert, G. C. E. 

 126 (1898) 814-. 



-- of 2 variables. Pokrovsky, P. Bll. Sc. 



Mth. 20 (1896) 86-. 

 ----- , addition theorem. Pokrowsky, 



P. [1895] D. Mth. Vr. Jbr. 4 (1897) 137-. 



335 



