4000 Algebraic Functions and their Integrals. General 4000 



Algebraic functions. Puiseux, V. Liouv. J. 



Mth. 15 (1850) 365-; 16 (1851) 228-. 

 (Puiseux). Canchy, A. L. C. B. 32 



(1851) 276-. 



. Hermite, C. C. B. 32 (1851) 458-. 



, application in geometry. Brill, A., & 



Nother, M. [1873] (vn) Mth. A. 7 (1874) 



269-. 

 , class. Schldmilch, 0. Grunert Arch. 



10 (1847) 67-. 

 , continuity and discontinuity, conditions. 



Gascheau, . Toul. Ac. Sc. Mm. 2 (1880) 



(Pt. 2) 122-. 

 and curves, property. Picard, E. C. B. 



91 (1880) 214-, 724-. 



, fundamental theorem. Voss, A. Mth. 



A. 27 (1886) 527-. 

 , number of arbitrary constants. Roch, G. 



[1864] Crelle J. 64 (1865) 372-. 



, property. Darboux, G. C. E. 94 

 (1882) 575-. 



, rationalisation. Polewski, S. Arch. 

 Mth. Ps. 69 (1883) 149-. 



, representation, approximate, by means 

 of rational functions. Bortolotti, E. Em. 



E. Ac. Line. Ed. 8 (1899) (Son. 1) 57-. 

 , , invariant. Noether, M. Mth. A. 



17 (1880) 263-. 



, Eiemann's theorem, demonstration. 

 Herz, N. [1881] Arch. Mth. Ps. 68 (1882) 

 14-. 



, singular points, application of Newton's 



polygon to theory. Baker, H. F. Camb. 

 Ph. S. T. 15 (1894) 403-. 



, theorem. Noether, M. Crelle J. Mth. 



92 (1882) 301-. 



, theory, development. Brill, A., < 

 Noether, M. D. Mth. Vr. Jbr. 3 (1894) 

 107-. 



, values, connexion between. Runge, C. 



Crelle J. Mth. 97 (1884) 337-. 



integrals, theorem. PtaSickij,I.L. Kharkov 

 Mth. S. Com. 1 (1889) 74-; Fschr. Mth. 

 (1888) 296-. 



Arbitrary function, determination. Cellerier, C. 

 Liouv. J. Mth. 8 (1843) 245-. 



functions, elimination. Hermite, C. B. A. 

 Ep. 42 (1872) 233-. 



Class of functions connected with 



=(*-a a ) (*-,)...(*-,), 



theory. Wellstein, J. Mth. A. 52 (1899) 



440-. 

 Coincidence of function with algebraic functions 



in infinite number of places. Schering, E. 



[1879] Gott. Ab. 27 (1881) (Mth.) 62 pp. 

 Continued fractions, new applications. Markov, 



A. St Pet. Ac. Sc. Mm. 3 (1896) No. 5, 



50pp. 

 Differentials, integrals of which are algebraic 



functions, form. Kapteijn, W. Amst. Ak. 



Vs. M. 17 (1882) 93-. 

 Expressions, integrals of which are algebraic. 



Liouville, J. [1832-37] Par. EC. Pol. J. 



22 cah. (1833) 124-, 149- ; Crelle J. 10 



(1833) 347-; C. E. 5 (1837) 330-. 

 Formula of Jacobi, demonstration. Brioschi, 



F. Tortolini A. 1 (1858) 117-. 



Fractional functions, decomposition and trans- 

 formation. Rangoni, L. [1827] (vm) Mod. 

 Mm. Ac. Sc. 1 (1833) (pte. 2) 254-. 



Functions in general, fundamental theories 

 established without reduction to the canon- 

 ical form. Tikhomandritskii, M. A. (xn) 

 Kharkov Mth. S. Com. (1883) 79-; Fschr. 

 Mth. (1885) 423. 



. with multiple periods. Casorati, F. C. 

 E. 57 (1863) 1018-. 



Goniometric functions, relation to certain alge- 

 braic expressions. Studnicka, F. J. Casopis 

 19 (1890) 249-; Fschr. Mth. (1891) 444. 



Identities, generalisation. Oltramare, G. Gen. 

 I. Nt. Mm. 16 (1886) No. 4, 109 pp. 



Integrals of algebraic differentials. Ramus, C. 

 Crelle J. 24 (1842) 69-. 



functions. Ostrogradsky, M. A. [1842] 



St Pet. Ac. Sc. Bll. 1 (1848) 113-. 



. Pellet, A. E. C. E. 90 (1880) 676-. 



, reduction to integrals of rational 



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

 14 (1881) 667-; 15 (1882) 165-. 



. , theorems. Poisson, S. D. Crelle 



J. 12 (1834) 89-. 



, theory. Jttrgensen, C. Kiob. Ov. 



(1839) 6-; Crelle J. 23 (1842) 126- ; N. Mg. 

 Ntvd. 3 (1843 ?) 85-. 



and transcendental formulae. Tortolini, 



B. G. Arcad. 56 (1832) 81-. 



. I^A X . Guic!iard,C. Par. EC. Norm. 



; JKM 



A. 5 (1888) 193-. 



Integration in finite explicit functions, deter- 

 mination of algebraic part. Piuma, C. M. 

 (vm) Tortolini A. 4 (1861) 154-. 



form of cubics and quartics sym- 

 metrical in x and -. Toropov, K. A. 



Kharkov Mth. S. Com. (1885) 3-; Fschr. 



Mth. (1885) 258. 

 , Jacobi-Mayer method, improvement. Lie, 



S. Christiania F. 15 (1873) 282-. 

 Inverse derived functions. Buquoy, G. von. 



Gilbert A. 67 (1821) 202-. 

 Inversion of system of functions. Lipschitz, R. 



Gott. Nr. (1870) 439-. 

 Isoperimetric equations and integrability. 



Brioschi, F. [1853] Mod. Mm. S. It. 25 



(1855) 205-. 

 Periodic function, calculation of coefficients 



from given mean values. Krttger, A. As. 



Nr. 82 (1873) 333-. 

 Periods of integrals. Marie, M. C. E. 36 



(1853) 437-. 

 Powers of functions, expansions, cases. Andre, 



D. [1877] Par. S. Mth. Bll. 6 (1878) 120-. 

 Product of several integrable and finite functions. 



Ascoli, G. Mil. I. Lomb. Ed. 12 (1879) 372-. 

 Eesolution of a class of functions. Jiirgensen, 



C. [1838] Kiob. Dn. Vd. Selsk. Afh. 8 

 (1841) 1-; Crelle J. 19 (1839) 84-. 



Sums depending on positive values of any 

 function. Cebysev, P. St Pe"t. Ac. Sc. Mm. 

 1 (1895) No. 7, 20pp.; Fschr. Mth. (1895) 

 441-. 



300 



