2410 Symmetric Functions 



Sums of powers of roots to (2n-l) th power, to 



construct polynomial from. Laguerre, E. 



Par. S. Mth. Bll. 5 (1877) 26-. 

 , Waring' s formula. Janni, V. 



Nap. Ed. 17 (1878) 27-. 

 , . Cayley,A. Mess. Mth. 



21 (1892) 133-. 

 , . Almeida Arez, J. B. d\ 



G. Teix. J. Sc. 14 (1900) 117- ; Fschr. Mth. 



(1900) 162. 

 , and Wronski's aleph function, 



Crocchi's proposition. Dickstein, S. Krk. 



Ak. (Mt.-Prz.) Pam. 12 (1886) (41)-; Fschr. 



Mth. (1886) 121. 



SYMMETEIC FUNCTIONS. 



Cauchy, A. L. [1824] Par. Mm. Ac. Sc. 9 



(1830) 104-. 



Conti, C. Padova N. Sag. 3 (1831) 90-. 

 Pioch, A. Brux. Ac. Bll. 2 (1835) 252-. 

 Transon, (Prof.) A. N. A. Mth. 9 (1850) 75-. 

 Dienger, J. Grunert Arch. 16 (1851) 471-. 

 Jaufroid, B. N. A. Mth. 12 (1853) 116-. 

 Brioschi, F. Tortolini A. 5 (1854) 313-, 422-. 

 Borchardt, C. W. N. A. Mth. 14 (1855) 26-. 

 Faa de Bruno, F. Tortolini A. 6 (1855) 338-, 



412-, 476-. 



Kronecker, L. Liouv. J. Mth. 1 (1856) 385-. 

 Betti, E. Crelle J. 54 (1857) 98-. 

 Cayley, A. Phil. Trans. (1857) 489-. 

 Roberts, M. Tortolini A. 3 (1860) 172- ; QJ. 



Mth. 4 (1861) 57-; (vm) A. Mt. 4 (1861) 



50-. 



Matthiessen, L. Z. Mth. Ps. 12 (1867) 322-. 

 Bonolis, A. G. Mt. 11 (1873) 321-. 

 Faa de Bruno, F. C. B. 76 (1873) 163-. 

 Isely, J. P. [1874] Neuch. S. Sc. Bll. 10 (1876) 



59-. 



Malet, J. C. [1874] Ir. Ac. T. 25 (1875) 337-. 

 Kapteyn, W. N. Arch. Wisk. 2 (* 1876) 73-. 

 Boschi, P. Bologna Ac. Sc. Mm. 7 (1876) 



569-. 



Kronecker, L. Berl. Ak. Mb. (1880) 936-. 

 Forsyth, A. R. Mess. Mth. 10 (1881) 44-. 

 Durfee, W. P. [1882] (xn) J. H. Un. Cir. [2] 



(1883) 23. 



Biehler, C. N. A. Mth. 3 (1884) 218-. 

 Ocagne, M. d\ G. Teix. J. Sc. 7 (1886) 133-. 

 Allardice, R. E. Edinb. Mth. S. P. 7 (1889) 



Worontzoff, . N. A. Mth. 10 (1891) 325-; 



12 (1893) 116-. 

 Kohn, G. Wien Ak. Sb. 102 (1893) (Ab. 2a) 



199-. 

 Brunei, . Bordeaux S. Sc. Mm. 4 (1894) 



Junker, F. Mth. A. 45 (1894) 1-. 



Metzler, W. H. L. Mth. S. P. 28 (1897) 



390-. 

 Gordan, P. Mth. A. 52 (1899) 501- ; D. Mth. 



Vr. Jbr. 8 (1900) (Heft 1) 178-. 

 algebraic theorem. Mertens, F. Wien Ak. Sb. 



106 (1897) (Ab. 2 a) 422-. 

 and alternating functions, genesis. Frisiani, P. 



Mil. Effem. As. (1846) 97-. 

 application to tetrahedra. Reiss, M. Quetelet 



Cor. Mth. 10 (1838) 229-. 



Symmetric Functions 2410 



associated quantities. Sylvester, J. J. C. E. 



98 (1884) 779-. 

 and binomial theorem. Bret, . Gergonne 



A. Mth. 4 (1813-14) 25-. 

 Brioschi's theorem. Sylvester, J. J. C. E. 



98 (1884) 858-. 

 calculation. Abbati, P. [1804] Mod. Mm. S. 



It. 12 (1805) 8-. 

 . Hammond, J. L. Mth. S. P. 13 (1881-82) 



79-. 



. Laurent, H. N. A. Mth. 6 (1887) 416-. 

 Cayley 's proof of rule for degree. Sylvester, 



J. J. Ph. Mg. 5 (1853) 199-. 

 class. Kapteijn, W. [1881] Arch. Mth. Ps. 67 



(1882) 102-. 



of permanent. Muir, T. Edinb. E. S. P. 

 11 (1882) 409-. 



classes. Garbieri, G. [1882] Yen. I. At. 1 



(1883) 33-. 



classification. Mathews, G. B. QJ. Mth. 25 



(1891) 127-. 



complete. Torelli, G, G. Mt. 5 (1867) 110-. 

 , and coefficients of an equation, corre- 

 spondence between. Crocchi, L. G. Mt. 20 



(1882) 301-. 

 "critical" and Spencian. Cockle, Jas. QJ. 



Mth. 4 (1861) 97-. 

 and a determinant of common occurrence. 



Trudi, N. Nap. Ed. 3 (1864) 121-. 

 determinant occurring in calculation. Gubler, 



E. Ziir. Vjschr. 35 (1890) 79-. 

 determination from coefficients. Kostka, C. 



[1875] Crelle J. Mth. 81 (1876) 281-. 

 development by sums of like powers. Janni, V. 



G. Mt. 23 (1885) 34-. 

 of differences of roots of an equation. Tannery, 



J. C. E. 98 (1884) 1420-. 

 elementary, relations between. Junker, F. 



Mth. A. 38 (1891) 91-. 

 , and sums of powers. Junker, F. Z. Mth. 



Ps. 41 (1896) 199-. 

 form (x, - X^P, #,, x 2 being roots. Roberts, 



M. N. A. Mth. 19 (1860) 23-. 

 formula concerning. Pesci, G. Bologna Ed. 



(1886-87) 49-. 

 formulae, 2. Petersen, J. P. C. (xn) Ts. Mth. 



6 (1876) 9-. 

 fundamental principle. Gergonne, J. D. 



Gergonne A. Mth. 3 (1812-13) 238-. 

 . Bret, . Gergonne A. Mth. 4 (1813- 



14) 25-. 



systems for. Vahlen, K. T. Acta Mth. 23 

 (1900) 91-. 



geometric representation. Spitzer, S. [1850] 



Haidinger Ab. 4 (1851) (Ab. 3) 1-. 

 and inverse operators. MacMahon, P. A. L. 



Mth. S. P. 15 (* 1883-84) 20-. 

 maximal and minimal values, proof of 



theorems of Cauchy. Terquem, 0. Liouv. 



J. Mth. 5 (1840) 37. 

 multiplication. Babczynski, T. Z. Mth. Ps. 



17 (1872) 147-. 

 . MacMahon, P. A. Mess. Mth. 14 (1885) 



164-. 

 of n variables, general theorem. Jung, G. C. 



E. 82 (1876) 988-. 

 new theorem. MacMahon, P. A. QJ. Mth. 



20 (1885) 365-. 



162 



