4060 Abelian Integrals 



depending on binomial algebraic equations, 



reduction. Dolbnia, I. P. Bee. Mth. 



(Moscou) 18 (1896) 647-; Bll. So. Mth. 20 



(1896) 156- . 

 and elliptic and hyperelliptic integrals, reduc- 



tion. Scheibner, W. Leip. Mth. Ps. B. 41 



(1889) 31-. 

 -- integrals, use in Diophantine analysis. 



Jacobi, G. G. J. Crelle J. 13 (1835) 353-. 

 evaluation, method. Richelot, F. J. C. B. 2 



(1836) 622-. 

 (and similar integrals) , expansion in continued 



fractions. Week, E. B. van. Am. J. Mth. 



16 (1894) 1-. 

 expansions in series for. Schlomilch, 0. X. 



Leip. Mth. Ps. B. 34 (1882) 1-. 

 expressible by logarithms. Goursat, E. C. B. 



118 (1894) 515-. 

 expression in terms of set of fundamental in- 



tegrals. Bolza, O. [1900] N. Y. Am. Mth. 



S. Bll. 7 (1901) 244, 252-. 

 extension of Legendre's relation to. Vahlen, 



K. T. Crelle J. Mth. 114 (1895) 47-. 

 and functions of 1st class, transformations. 



Pokrovskij, P. M. Bee. Mth. (Moscou) 15 



(1891) 397-; Bll. Sc. Mth. 17 (1893) 85-. 

 fundamental loci of functions inverse to. 



Casorati, F. Acta Mth. 8 (1886) 360-. 

 most general relations among. Konigsberger, L. 



[1875] Crelle J. Mth. 81 (1876) 193-. 

 genus of certain class, determination. Dolbnia, 



J. Bll. Sc. Mth. 19 (1895) 272-; 21 (1897) 



243-. 

 1, direct study. Dolbnia, J. Par. EC. Norm. 



A. 15 (1898) 393-. 

 geometrical representation. Cayley, A. 



Abelian Integrals 4060 



3rd kind. Emmanuel, D. Par. EC. Norm. A. 

 8 (1879) 299-. 



, interchange of argument and para- 

 meter paths. Graf, J. H. Bern Mt. (1877) 

 64-. 



of different kinds, forms. Appell, P. Toul. 



Fac. Sc. A. 7 (1893) A, 4 pp. 

 mechanical application. Neumann, C. Crelle 



J. 56 (1859) 46-. 

 moduli, choice. Borchardt, C. W. C. B. 88 



(1879) 834-. 

 1st order. Cayley, A. Crelle J. Mth. 98 



(1885) 95-. 

 -- , expressible as sum of two elliptic inte- 



grals. Burnside, W. L. Mth. S. P. 23 



(1892) 173-. 



, reduction to normal form. Jacobi, 

 C. G. J. Crelle J. 55 (1858) 1-. 



-- , 3rd species. Eoch, G. [1865] Crelle J. 



65 (1866) 42-. 

 -- , transformation. Eichelot, F. J. Crelle 



J. 16 (1837) 221-, 226-, 285-. 

 -- , . Krause, M. Acta Mth. 3 (1883) 



153- ; Crelle J. Mth. 95 (1883) 256-. 

 -- , of 2nd order. Richelot, F. J. Berl. 



Mb. (1866) 412-. 

 jp = 3, reduction to elliptic integrals. Gilespie, 



W. Am. J. Mth. 22 (1900) 259-. 

 periodicity moduli. K$pinski, S. Krk. Ak. 



(Mt.-Prz.) Bz. 17 (1900) 63-; Crc. Ac. Sc. 



Bll. 



Mg. 6 (1853) 414-. 

 nd hi 



and higher integrals of 3rd kind, interchange 



of parameter and argument. Jacobi, C. G. J. 



Crelle J. 32 (1846) 185-. 

 imaginary numbers resulting from. Efimov, 



M. T. Kazan S. Ps.-Mth. Bll. 4 (1895) 



(Prof.) 72-. 

 independence of zeros in Jacobian function. 



Martins da Silva, J. A. G. Teix. J. Sc. 5 



(*1883) 3-. 

 integration in finite form, general theorems 



for. Ptaszycki, J. Prace Mt.-Fiz. 11 (1900) 



23- ; Fschr. Mth. (1900) 452. 

 inversion. Weber, H. Crelle J. 70 (1869) 



314-. 

 . Appell, P. Liouv. J. Mth. 1 (1885) 



. Goursat, E. C. B. 115 (1892) 787-. 



Goteb. Hndl. 30 (1895) 



(1898) 270-. 



, differential equations for. Fuchs, L. 

 Crelle J. 73 (1871) 324-. 



-- as functions of a branch-point. Fuchs, 



R. Crelle J. Mth. 119 (1898) 1-. 

 Ph. ------ parameter. Fuchs, L. [1869] 



Crelle J. 71 (1870) 91-, 128-. 



, relations. Konigsberger, L. Gott. Nr. 

 (1875) 327-. 



-- , . Herz, N. [1881] Arch. Mth. Ps. 



68 (1882) 196-. 

 periods, differential equations for. Wiltheiss, E. 



Mth. A. 34 (1889) 150-. 

 properties, general. Abel, N. H. [1826-29] 



Par. Mm. Sav. Etr. 7 (1841) 176- ; Crelle J. 



3 (1828) 313- ; 4 (1829) 200-. 



, . Mainardi, G. Mil. G. I. Lomb. 7 

 (1855) 426-. 



1st rank, inversion. Dolbnia, J. P. Fschr. 



Mth. (1898) 391-. 

 reducible. Kluyver, J. C. Amst. Ak. Vs. 7 



(1899) 425- ; Amst. Ak. P. 1 (1899) 449-. 

 reduction. Malet, 



. Hallgren, E. 

 77 pp. 



inversions, representation. Dillner, G. Bor- 



deaux S. Sc. Mm. 5 (1883) 291-. 

 and Jacobi's equations. Cayley, A. Camb. 



and Dubl. Mth. J. 3 (1848) 51-. 

 1st kind, number. Elliot, Z. Par. EC. Norm. 



A. 5 (1876) 399-. 

 -- , . Picard, E. Bll. Sc. Mth. 14 (1890) 



131-. 

 -- , periodicity moduli, fundamental rela- 



tions. Casorati, F. A. Mt. 3 (1869-70) 1-. 



and 2nd kinds, expansion in series. Konigs- 

 berger, L. [1875] Mth. A. 9 (1876) 487-. 



97-. 



J. C. Crelle J. 76 (1873) 



. Picard, E. C. B. 93 (1881) 696-. 



. Kotanyi, L. [1883] (x) Wien Ak. Sb. 88 

 (1884) (Ab. 2) 401-. 



. Hermite, C. Edinb. B. S. P. 12 (1884) 

 642-. 



. Poincare, H. C. B. 99 (1884) 853- ; Par. 

 S. Mth. Bll. 12 (1884) 124-. 



. Goursat, E. Par. S. Mth. Bll. 13 (1885) 

 143-. 



. Gomes Teixeira, F. G. Teix. J. Sc. 8 

 (1887) 164-. 



. Pick, G. Mth. A. 32 (1888) 443-. 



to algebraic logarithmic functions. Konigs- 

 berger, L. Mth. A. 11 (1877) 119-. 



332 



