3270 Multiple Integrals 



Cases. Liouville, J. Liouv. J. Mth. 4 (1859) 



155-. 

 . Taylor, H. M. Mess. Mth. 5 (1876) 



. Sersawy, F. Arch. Mth. Ps. 64 (1879) 



30-. 

 . Staeckel, . fill. Sc. Mth. 21 (1897) 



31. 

 Change of variables. Catalan, E. C. Par. S. 



Phlm. PV. (1839) 123-. 

 . Baehr, G. F. W. Arch. Mth. Ps. 



41 (1864) 453-. 

 Class. Tchebicheff, P. Liouv. J. Mth. 8 (1843) 



235-. 

 . Liouville, J. Liouv. J. Mth. 1 (1856) 



82-. 

 . Lipschitz, E. Crelle J. Mth. 101 (1887) 



214-. 

 , numerical values. Hamilton, (Sir) W. R. 



Ph. Mg. 14 (1857) 375-. 

 Classes. Elliott, E. B. [1876-77] L. Mth. S. 



P. 8 (1877) 35-, 146-. 

 Convertent functions. Cockle, (Sir) J, [1868] 



Manch. Lt. Ph. S. P. 8 (1869) 2-; 9 (1870) 



86-; 10(1870)1-. 

 Curvilinear coordinates, Stokes' s theorem. 



Padova, E. Mil. I. Lomb. Ed. 25 (1892) 



1021-. 

 Determination by transformation of coordinates. 



Cauchy, A. L. C. E. 13 (1841) 34-. 

 Differentiation with regard to parameter on 



which limits also depend. Zindler, K. Wien 



Ak. Sb. 106 (1897) (Ab. 2a) 359-. 



Double integrals. 



Schlffinilch, 0. Grunert Arch. 11 (1848) 174-. 

 Dienger, J. Grunert Arch. 13 (1849) 286-. 

 Steen, A. Kiob. Dn. Vd. Selsk. Skr. 1 (1849) 



333-. 



Besge, V. A. Liouv. J. Mth. 3 (1858) 324. 

 Le Cordier, P. C. E. 66 (1868) 707-. 

 Besso, D. G. Mt. 10 (1872) 79-. 

 DM Bois-Reymond, P. [1882] Crelle J. Mth. 



"' ""33)273-. 



Goursat, E. C. E. 96 (1883) 1304-. 



Arzela, C. Bologna Ac. Sc. Mm. 2 (1891) 



133. 



Pochhammer, L. Mth. A. 41 (1893) 179-. 

 of algebraic functions, reduction. Picard, E. 



C. E. 126 (1898) 1116-. 

 apparently with two values. Puzyna, J. [1883] 



(xn) Krk. Ak. (Mt.-Prz.) Pam. 9 (1884) 



and binary intervals, theory. Meray, C. Par. 



EC. Norm. A. 16 (1899) 193-. 

 calculation, approximate. Minding, E. F A 



Crelle J. 6 (1830) 91-. 

 , case. Callandreau, 0. C. E. 96 (1883) 



1125. 

 Cases. Roberts, W. A. Mt. 3 (1869-70) 



327-. 

 . Didon, F. Par. EC. Norm. A. 7 (1870) 



. Orlow, G.A. N. A. Mth. 1 (1882) 311-. 

 Cauchy's theorem. Kluyver, J. C. Fschr. 

 Mth. (1897) 258. 



Double Integrals 3270 



class. Goursat, E. Acta Mth. 5 (1884) 97-. 



including Fourier's. Du Bois-Reymond, P. 

 Crelle J. 69 (1868) 65-. 



Crofton's theorem, corollary. Hoppe, R. C. 



E.70 (1870) 1394- ; Arch. Mth. Ps. 55 (1873) 



426-. 

 differentiation and integration. Bierens de 



Haan, D. Amst. Vs. Ak. 5 (1871) (Ntk.) 



53-, 65-; Arch. Neerl. 6 (1871) 329-. 

 of explicit irrational functions, theory. Bier- 



mann, O. Wien Ak. Sb. 98 (1890) (Ab. 2a) 



340-. 

 formulae, integration. Fuss, N. [1826] St Pt. 



Ac. Sc. Mm. 11 (1830) 294-. 

 Fourier's theorem, Boole's and other proofs. 



Alexander, P. Edinb. Mth. S. P. 3 (1885) 



45-. 

 geometric demonstration. Chasles, M. Liouv. 



J. Mth. 3 (1838) 10-. 



evaluation. Collignon, E. As. Fr. C. E. 3 

 (1874) 1193-. 



integration. Sylvester, J. J. Ph. Mg. 14 



(1839) 298-. 

 inversion. Appell, P. Am. J. Mth. 19 (1897) 



377-, 382. 



. Le Roux, J. C. E. 130 (1900) 882-. 

 of 2nd kind in theory of algebraic surfaces. 



Picard, E. [1897] Liouv. J. Mth. 5 (1899) 



5. 

 maxima and minima. Kobb, G. Stockh. 6fv. 



(1890) 385- ; Fschr. Mth. (1890) 382 ; Acta 

 Mth. 16 (1892-93) 65-; 17 (1893) 321-. 



and their periods, elementary theory. Marie, 



M. C. E. 75 (1872) 576-, 614-, 660-. 

 Poisson's theorem, proof. Roberts, W. Liouv. 



J. Mth. 11 (1846) 210-. 

 properties. Rodrigues, (Dr) . Par. S. Phlm. 



Bll. (1815) 34-. 

 of rational functions, residues. Picard, E. 



C. E. 124 (1897) 433-. 

 reduction, and new invariant in theory of 



algebraic surfaces. Picard, E. C. E. 126 



(1898) 297-. 



to products of simple integrals. Schlomilch, 

 O. Z. Mth. Ps. 9 (1864) 205-. 



quadratures. Winckler, A. [1851] Crelle 



J. 45 (1853) 102-. 

 residues. Poincare, H. C. E. 102 (1886) 202- ; 



Acta Mth. 9 (1887) 321-. 



(Poincare). Marie, M. N. A. Mth. 10 



(1891) 77-. 



, theory. Marie, M. C. E. 75 (1872) 695-, 

 751-. 



returning to same form after transformation of 

 variables. Jacobi, C. G. J. Crelle J. 15 

 (1836) 193-. 



theory. Harnack, A. Mth. A. 26 (1886) 566-. 



. Pringsheim, A. Munch. Ak. Sb. 28 (1899) 

 59-. 



, Green's and Cauchy's theorems. Prings- 

 heim, A. Munch. Ak. Sb. 29 (1900) 39-, 

 268-. 



and invariant of two triangles. Le Roux, 

 . Par. S. Mth. Bll. 28 (1900) 168-. 



transformation. Jacobi, C. G. J. [1827-32] 

 Crelle J. 2 (1827) 234-; 8 (1832) 253-, 321- ; 

 10 (1833) 101-. 



284 



