4800 



Differential Equations. General 



4800 



Theorem of Picard, demonstration. Borel, E. 



C. B. 122 (1896) 1045-. 

 , (Borel). Picard, E. C. B. 122 



(1896) 1048. 

 Theorems. Vivanti, G. G. Mt. 22 (1884) 243-, 



378. 



Theory. Schou, E. C. B. 125 (1897) 763-. 

 Transcendental functions. Vivanti, G. G. 



Mt. 23 (1885) 96-; Mil. I. Lomb. Ed. 32 



(1899) 569-. 



Zeros. Borel, E. Acta Mth. 20 (1897) 357-. 

 , position. Witting, A. Z. Mth. Ps. 30 



(1885) 274-. 

 ^ (a, b) and x ( a &)> elementary properties. 



Lerch, M. Casopis 24 (1895) 25-, 118-, 



228-; Fschr. Mth. (1895) 217-. 



Differential equations. 



4800 General. (See also 8080 

 Connexes.) 



Algebraic equations. Casorati, F. A. Mt. 9 



(1878-79) 41-, 106-. 

 , number of independent transcendentals 



belonging to. Koenigsberger, L. Mth. A. 



30 (1887) 299-. 

 Analogues. Bourlet, C. Par. EC. Norm. A. 



16 (1899) 333-. 



Analytical remarks on Ouroussof ' s work. Mind- 

 ing, E. F. A. [1865] St P<t. Ac. Sc. Bll. 9 



(1866) 48-. 



Application of curve systems to graphic inte- 

 gration. Ldska, T. Prag Sb. (1890) 1 (Mth.- 



Nt.) 222-. 

 Asymptotic integrals. Boussinesq, J. C. E. 



94 (1882) 208-. 

 Bibliographical note. Mansion, P. Brux. S. 



Sc. A. 15 (1891) (Pt. 1) 32-, 60, 105. 

 Case. Cayley, A. Manch. Ph. S. P. 2 (1860- 



62) 193. 

 Composition from given integral equation. 



Bierens de Haan, D. Amst. Ak. Vh. 18 



(1879) 37 pp. 

 Conditions that primitive may have degree 



lower than normal. Casorati, F. Mil. I. 



Lomb. Ed. 10 (1877) 770-. 

 Conjoint differential equations, integration. 



Starkov, A. N. Es. S. Nt. Mm. (Mth.) 2 



(*1879). , 

 Continuity of functions representing integrals 



of a system. Cauchy, A. L. C. E. 23 



(1846) 702-. 

 Deduction from graphs. Warder, JR. B. 



Science 4 (1896) 345. 

 Determination of four functions to satisfy a 



certain equation. Vivanti, G. Palermo 



Cir. Mt. Ed. 6 (1892) 100-. 

 Differential and difference equations, connexion 



between. Mellin, H. Acta Mth. 9 (1887) 



137-. 

 functions, equations of condition. Stockier, 



F. de B. G. Lisb. Mm. Ac. Sc. 2 (1799) 196-. 

 Elimination of arbitrary functions. Fais, A. 



Bologna Ac. Sc. Mm. 9 (1878) 649-. 



Equation for confocal conic system, integration. 

 Guimaraes, E. Lisb. J. Sc. Mth. 5 (1898) 

 105-. 



of curve of any order. Sylvester, J. J. C. 

 E. 103 (1886) 408- ; Nt. 34 (1886) 365-. 



Equations. Schmidten, H. G. Kiob. Ov. 

 (1825-26) 2-. 



and applied mathematics, historical sketch. 

 Naetsch, E. Giving. 41 (1895) 655-. 



of conies. Monge, G. Par. EC. Pol. Cor. 

 2 (1809-13) 51-. 



. Muir, T. Ph. Mg. 21 (1886) 143-. 



. Elliott, E. B. Mess. Mth. 19 (1890) 



5-. 



determining form of roots of algebraic equa- 

 tions. Boole, G. Phil. Trans. 154 (1864) 

 733-. 



, general integral of which is algebraic, 

 class. Picard, E. C. E. 120 (1895) 402-. 



having fundamental solutions, theory. 

 Guldberg, A. Crelle J. Mth. 115 (1895) 

 111-. 



obtained by elimination of 2 arbitrary 

 functions. Worms de Eomilly, P. Par. S. 

 Mth. Bll. 8 (1880) 64-. 



with periodic integrals. Hill, G. W. A. 

 Mth. 3 (1887) 145-. 



and their integrals. Raabe, J. L. Baum- 

 gartner Z. 5 (1829) 27-. 



Functional and differential equations, cases. 



Thiele, T. N. (xn) Ts. Mth. 4 (1868) 109-, 



180- ; 5 (1869) 62-. 

 Functions defined by differential equations, 



residues. Petrovitch, M. Mth. A. 48 (1897) 



75-; Prag Sb. (1898) (Mth.-Nt.) No. 6, 



24 pp. 



satisfying algebraic equation, expansion. 

 Hurwitz, A. Par. EC. Norm. A. 6 (1889) 

 327-. 



differential equation, expansion. Gomes 



Teixeira, F. Par. EC. Norm. A. 2 (1885) 



321- ; 4 (1887) 107-. 

 Geometric meaning. Cunningham, A. QJ. 



Mth. 14 (1877) 226-; Nt. 38 (1888) 318-. 

 Imaginary integrals and their advantages. 



Cauchy, A. L. C. E. 23 (1846) 563-. 

 Integrable equation, derivation by Liouville's 



method. Thomae, C. J. Gott. Nr. (1874) 



249-. 

 Integrals, algebraic, relations. Koenigsberger, 



L. Crelle J. Mth. 115 (1895) 23-. 



of equations about essential singularities 

 (viz. "normal" series in Poincar^'s sense). 

 Bajewski, J. Krk. Ak. (Mt.-Prz.) Pam. 17 

 (1890) 166- ; Crc. Ac. Sc. Bll. (1890) 62-. 



, rectilinear, and complete integrals of a 



system of equations, relations between. 



Cauchy, A. L. C. E. 23 (1846) 779-. 

 , relations. Fuchs, L. Berl. Ak. Sb. (1887) 



1077-. 

 , , algebraic. Kimigsberger, L. [1877-80] 



Crelle J. Mth. 84 (1878) 284-; 91 (1881) 



199-. 



of systems of ordinary or partial differential 

 equations and expansions of these integrals 

 in series. Cauchy, A. L. C. E. 15 (1842) 

 101-, 141-. 



354 



