3270 



Multiple Integrals 



3270 



transformation. Cayley, A. Mess. Mth. 4 



(1875) 92-. 



. Berger, A. Stockh. Ofv. (1887) 153-. 

 . Stolz, 0. Mh. Mth. Ps. 9 (1898) 316-, 



371; 10 (1899) 96. 



formula. Scheibner, W. Leip. Mth. Ps. B. 

 36 (1884) 185-. 



, Euler's. Plana, G. Brux. Ac. Bll. 10 



(1843) 303-. 

 , general. Winckler, A. Wien D. 20 (1862) 



97-. 



by Green's theorem. Gmeiner, J. A. Mh. 

 Mth. Ps. 4 (1893) 277-. 



and triple integrals, simultaneous substitutions, 

 theory. Unferdinger, F. Wien Sb. 63 (1871) 

 (Ab. 2) 773-. 



, transformation. Piola, G. Mod. 

 Mm. S. It. 20 (1828) 272-. 



, . Tait, P. G. [1873] Edinb. E. 



S. P. 8 (1875) 209-. 



4>(ax m by n )xP 

 <f> (ax m by n ) 



l dxdy, 



Raabe, J. L. Crelle J. 37 (1848) 345-. 



~c fb 



1:1: 



6 J o V(c 2 - /t 2 ) (/t 2 - 6 2 ) (c 2 - v 2 ) (6 2 - v 2 ) 

 Huberts, W. Liouv. J. Mth. 15 (1850) 238-. 



Equality. Besge, V. A. Liouv. J. Mth. 3 

 (1858) 416. 



Evaluation. Ellis, R. L. Camb. Mth. J. 4 

 (1845) 1-. 



, case. Gregory, D. F. Camb. Mth. J. 2 

 (1841) 215-. 



, process. Arndt, F. Grunert Arch. 5 (1844) 

 443-. 



Expansibility of quotient of two definite in- 

 tegrals of form idxdy...dz. Schlafti, L. 



Crelle J. 67 (1867) 183-. 

 Expansion. Schlomilch, 0. Schlomilch Z. 1 



(1856) 75-. 

 Formula, demonstration. Thomson, (Sir) W. 



Liouv. J. Mth. 10 (1845) 137-. 

 , (Thomson). Liouville, J. Liouv. J. 



Mth. 1 (1856) 445-. 

 , Fourier's, generalised by Liouville. Popov, 



A. T. (xii) Kazan Un. Mm. (1848) (Bk. 4) 3-. 

 Frullanian integrals. Elliott, E. B. L. Mth. 



S. P. 15 (*1883-84) 12-. 

 Integral expressing area of circle and of 



spherical triangle. Schlafti, L. Liouv. J. 



Mth. 20 (1855) 359-. 

 Integrals of area and volume, transformations 



and values. Tortolini, B. G. Arcad. 80 



(1839) 13-; 82 (1840) 97-. 



with 3 complex variables. Picard, E. C. 

 E. 108 (1889) 132-. 



of Jacobi. Zinin, N. N. Vars. S. Nt. Tr. 

 (1897) (Ps. C.) Fasc. 1, No. 3, ii. 



any order, and their periods, elementary 



theory. Marie, M. C. E. 75 (1872) 1078-, 

 1247-. 



Integrals in probability theory, two. Czuber,E. 

 Mh. Mth. Ps. 2 (1891) 119-. 



representing products and powers of simple 

 definite integrals. Raabe, J. L. [1847] Ziir. 

 Mt. 1 (Heft 2) (1847-48) 29-; Crelle J. 48 

 (1854) 137-. 



in theory of attractions. Cayley, A. Camb. 

 and Dubl. Mth. J. 2 (1847) 219- ; 7 (1852) 

 174-. 



unaltered in form by transformation of the 

 variables. Gundelfinger, S. [1880] Crelle 

 J. Mth. 91 (1881) 215-. 



, value of which is affected by order of 



integration. Decker, G. Grunert Arch. 19 



(1852) 403- ; 22 (1854) 413-. 

 Inversion. Volterra, V. Em. E. Ac. Line. 



Ed. 5 (1896) (Seat. 1) 289-. 

 , mode. Appell, P. C. E. 124 (1897) 213-. 

 Limits. MacColl, H. L. Mth. S. P. 16 (1884- 



85) 142-. 

 Line and surface integrals. Peirce, B. 0. Am. 



Ac. P. 26 (1891) 20-. 

 , surf ace and volume integrals, relation among. 



Tait, . Edinb. E. S. P. 16 (1890) 257. 

 Maxima and minima, criteria. Sabinine, G. 



[1869] St Pet. Ac. Sc. Bll. 15 (1871) 70-. 

 Mean values of functions. Cauchy, A. L. C. 



B. 18 (1844) 558-; 20 (1845) 119-, 212- ; 26 



(1848) 549-, 624-, 666-; 27 (1848) 6-, 37-; 



29 (1849) 341-. 

 Minimum. Lebesgue, H. C. E. 131 (1900) 



935-. 

 Multiple Gaussian sums. Weber, H. [1871] 



Crelle J. 74 (1872} 14-. 



and single integrals. Nanson, E. J. Mess. 

 Mth. 26 (1897) 119-. 



Ostrogradskii's formulae. Zinin, N. N. Eec. 



Mth. (Moscou) 15 (1891) 645-; Fschr. Mth. 



(1891) 304-. 

 Problem. Zinine, N. N. Fschr. Mth. (1888) 



308-. 

 Eeduction. Catalan, E. C. Liouv. J. Mth. 4 



(1839) 323-; 6 (1841) 81-; 8 (1843) 239-; 



Brux. Mm. Cour. 4, 14 (1841) 47 pp. 



(error in Catalan's paper, 1841). Boole, G. 

 Camb. Mth. J. 3 (1843) 277-. 



. Chelini, D. G. Arcad. 94 (1843) 49-. 

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



289-. 

 . Enneper, A. Gott. Nr. (1867) 164- ; Z. 



Mth. Ps. 15 (1870) 121-. 

 . Letnikov, A. V. Eec. Mth. (Moscou) 14 



(1890) 303- ; Fschr. Mth. (1889) 288. 

 . Nekrasov, P. A. [1891] Eec. Mth. (Mos- 

 cou) 16 (1893) 81-; Fschr. Mth. (1891) 305. 

 . La Vallee-Poussin, C. J. de. C. E. 127 



(1898) 950-. 

 , application of general differentiation. 



Nekrasov, P. A. Eec. Mth. (Moscou) 14 



(1890) 410- ; Fschr. Mth. (1889) 288-. 

 , cases. Raabe, J. L. Crelle J. 28 (1844) 



19-. 

 , -. Schaar, M. Brux. Ac. Bll. 15 (1848) 



(pte. 2) 501-. 

 , . Genocchi, A. Tortolini A. 8 (1857) 



284-. 

 , . Schlomilch, 0. Leip. B. 9 (1857) 67-; 



Liouv. J. Mth. 2 (1857) 206-. 



285 



