4060 Abelian Integrals 



reduction to algebraic logarithmic functions, 

 inexactitude of Koenigsberger's rule for value 

 of integral. Ptaszycki, J. Mth. A. 16 (1880) 

 264-. 



of class, to elliptic integrals. Kowalevski, S. 

 Acta Mth. 4 (1884) 393-. 



to elliptic functions. Cayley, A. C. E. 85 

 (1877) 265-, 373-, 426-, 472-. 



, cases. Brioschi, F. C. B. 85 



(1877) 708-. 

 , example. Hermite, C. (xn) Brux. 



S. Sc. A. 1 (1877) (Pt. 2) 1-. 

 and hyperelliptic integrals. Konigs- 



berger, L. Mth. A. 15 (1879) 174-. 

 integrals. Konigsberger, L. Crelle 



J. Mth. 85 (1878) 273-. 

 . Picard, E. C. E. 93 (1881) 



1126- ; 94 (1882) 1704-. 

 . Ungar, M. Wien Ak. Sb. 83 



(1881) (Ab. 2) 759-. 

 . Picard, E. Par. S. Mth. Bll. 12 



(1884) 153-. 

 . Bolza, 0. Freiburg B. 8 (*1882- 



85) 330-. 

 . Biermann, 0. Wien Ak. Sb. 



105 (1896) (Ab. 2o) 924-. 

 . Brun, F. de. Stockh. Ofv. (1897) 



413-. 



, relation to complex multiplication 



of elliptic integrals. Konigsberger, L. [1878] 

 Crelle J. Mth. 86 (1879) 317-. 



by transformation of 3rd degree. 



Brioschi, F. Par. EC. Norm. A. 8 (1891) 



227-. 

 . Bolza, 0. Mth. 



A. 50 (1898) 314- ; 51 (1899) 478-. 

 functions of 1st, 2nd and 3rd kinds. 



Hermite, C. Bll. Sc. Mth. As. 7 (1883) 36-. 



of group. Alth, G. von. Wien Ak. Sb. 95 

 (1887) (Ab. 2) 702-. 



to lower integral forms, especially elliptic. 

 Konigsberger, L. [1879] Crelle J. Mth. 89 

 (1880) 89-. 



normal form, cases. Ptaszycki, J. Mth. 



A. 33 (1889) 600- ; Prace Mt.-Fiz. 2 (1890) 



' , demonstration. Malet, J. C. [1874] 



Crelle J. Mth. 79 (1875) 176-. 

 integrals. Ungar, M. [1882] Wien 



Ak. Sb. 86 (1883) (Ab. 2) 893-. 



of number of periods, in particular for curves 

 of 2nd genus. Picard, E. [1882] Par. S. 

 Mth. Bll. 11 (1883) 25-. 



by transformation of 4th degree. Bolza, 0. 

 Mth. A. 28 (1887) 447-. 



, and transformation of Fuchsian functions. 



Poincare, H. C. E. 102 (1886) 41-. 

 related to intersection curve of two surfaces, 



covariants. White, H. S. Mth. A. 36 (1890) 



597-. 

 Eiemann's theory (Neumann). Bertini, E. 



Palermo Cir. Mt. Ed. 6 (1892) 165-. 

 1st species. Rink, H. J. Z. Mth. Ps. 29 



(1884) 272-. 

 , plane curves rectifiable by. Broden, T. 



Stockh. Ak. Hndl. Bh. 15 (Afd. 1) (1890) 



No. 5, 26 pp. 



Abel's Theorem 4060 



2nd and 3rd species. Staude, 0. Acta Mth. 8 



(1886) 81-. 



. Krause, M. A. Mt. 15 (1887-88) 



187-. 

 , addition theorems. Jacobi, G.G.J. 



Crelle J. 30 (1846) 121-. 

 and 1st order, representation by 



integrals of 1st species. Schirdewahn, G. 



Z. Mth. Ps. 34 (1889) 355-, 385. 

 3rd species. Eoch, G. [1866] Crelle J. 68 



(1868) 170-. 



, attached to algebraic curves without 

 singularities. Pick, G. [1886] Wien Ak. Sb. 

 94 (1887) (Ab. 2) 367-. 



theorem of Weierstrass, demonstration. Bel- 



jankin, I. Kazan S. Ps.-Mth. Bll. 9 (1900) 



35-. 

 theorems. Malet, J. C. [1874] Ir. Ac. T. 25 



(1875) 279-. 

 theory. Bouquet, . C. E. 67 (1868) 989-; 



Par. Mm. Sav. fttr. 21 (1875) 675-. 

 . Goursat, E. C. E. 97 (1883) 1281-. 

 . Dolbnia, I. Kazan S. Ps.-Mth. Bll. 3 



(1893) 1-, 57-, 109-. 



of a class. Pick, G. A., & Ungar, M. 

 [1880] Wien Ak. Sb. 82 (1881) (Ab. 2) 893-. 



transformation. Elliot, Z. Par. 6c. Norm. 



A. 9 (1880) 167-. 



. Heymann, W. Z. Mth. Ps. 33 (1888) 31-. 

 , case. Toropov, K. A. [1887] Kharkov 



Mth. S. Com. 1 (1889) 82-; Fschr. Mth. 



(1887) 477-. 



equation of 2nd order and coefficients of 

 linear equations. Eisenstein, G. Crelle J. 

 44 (1852) 261-. 



problem, reduction. Konigsberger, L. Mth. 

 A. 13 (1878) 540-. 



Abelian system of differential equations. Ro- 

 berts, E. R. W. E. S. P. 57 (1895) 301-. 



Abel's formula. Roberts, W. Liouv. J. Mth. 

 16 (1851) 143-. 



. Bertrand, J. Tortolini A. 1 (1858) 



156-. 



, demonstration. Ovidio, E. d'. G. Mt. 



6 (1868) 37-. 



, generalisation. Sonin, N. N. Es. S. Nt. 



Mm. (Mth.) 5 (1884). 



and Jacobi's theorem, demonstration. Mai- 

 nardi, G. [1844] Mod. S. It. Mm. 23 (1846) 

 171-. 



problem, Letnikov's solution. Liventsov, 

 A. I. [1878] (xn) Eec. Mth. (Moscou) 9 

 (1878-81) (Pt. 1) 114-. 



problems. Formenti, C. Mil. I. Lomb. Ed. 

 8 (1875) 276-. 



Abel's theorem. 



Jacobi, C. G. J. Crelle J. 9 (1832) 99. 

 Liouville, J. C. E. 17 (1843) 720. 

 Cremona, L. Tortolini A. 7 (1856) 99-. 

 Cayley, A. Tortolini A. 8 (1857) 201-. 

 Genocchi, A. Tortolini A. 1 (1858) 33-. 

 Heine, H. E. [1862] Crelle J. 61 (1863) 276-. 

 Konigsberger, L. [1880] Crelle J. Mth. 90 

 (1881) 109-. 



333 



