3220 Infinite Series, etc. 



3220 Infinite series; infinite pro- 

 ducts and other infinite pro- 

 cesses. (See also 5610, 5620.) 



INFINITE SEEIES. 



Fontana, G. Verona S. It. Mm. 2 (1784) 386-. 

 Paoli, P. Verona S. It. Mm. 4 (1788) 429-. 

 Parseval, M. A. [1799] Par. Mm. Sav. Etr. 1 



(1806) 638-. 

 Bianchi, G. [1844] Mod. Mm. S. It. 23 (1846) 



239-. 



Malmsten, C. J. Crelle J. 38 (1849) 1-. 

 Dienger, J. Crelle J. 38 (1849) 266-, 331-. 

 Tremoil, . N. A. Mth. 9 (1850) 66. 

 Bjorling, E. G. Stockh. Ofv. 10 (1853) 147-. 

 Schlomilch, 0. Schlomilch Z. 1 (1856) 180- ; 



5 (I860) 132-. 



Kinkelin, H. Bern Mt. (1858) 88-. 

 Greer, H. R. QJ. Mth. 3 (1860) 262-, 370-. 

 Isely, M. Neuch. Bll. 6 (1861-63) 356-. 

 Cockle, Jas. [1863] (n) Mess. Mth. 2 (1864) 



196-. 

 Lindman, C. F. Arch. Mth. Ps. 50 (1869) 



219-. 



Enneper, A. Z. Mth. Ps. 15 (1870) 47-. 

 Schlomilch, 0. X. Leip. Mth. Ps. B. 29 (1877) 



101-. 

 Barbour, L. G. Des Moines Anal. 8 (1881) 



191-. 



West, E. Liouv. J. Mth. 7 (1881) 111-. 

 Catalan, E. C. Liege S. Sc. Mm. 12 (1885) 



No. 2, 148-, 152-, 206-, 282-, 294-. 

 Cesdro, E. G. Teix. J. Sc. 7 (1886) 171- ; 8 



(1887) 15-. 



Biehler, C. N. A. Mth. 6 (1887) 243-. 

 Gutzmer, A. G. Teix. J. Sc. 8 (1887) 81-. 

 Studnicka, F. J. Casopis 16 (1887) 81-; 



Fschr. Mth. (1887) 227. 

 Weyr, E. G. Teix. J. Sc. 8 (1887) 97-. 

 Catalan, E. Brux. Ac. Bll. 18 (1889) 41-. 

 Tauber, A. Mh. Mth. Ps. 8 (1897) 273-. 

 Absolutely summable series, series t (M) and 



analytical continuation. Borel, E. C. E. 



131 (1900) 830-. 

 Algebraic series. Sidler, G. Ziir. Vjschr. 1 



(1856) 180- ; Bern Mt. (1899) 13-. 

 , new. Wallace, J. Silliman J. 7 (1824) 



278-; 9 (1825) 98-. 

 . (Wallace). B. (viAdds.) Silliman 



J. 8 (1824) 131- ; 9 (1825) 293-. 

 Analytic series. Svanberg, J. Stockh. Ak. 



Hndl. 22 (1801) 30-. 



, genetic explanation. Barfuss, F, W. 

 Grunert Arch. 8 (1846) 387-. 



Applications to arithmetic. Sardi, C. G. Mt. 

 7 (1869) 257-. 



Approximation to geometric means by series of 

 arithmetical and harmonic means. Mathieu, 

 J. J. A. N. A. Mth. 18 (1879) 529-. 



series. Meyer, A. N. Ts. Mth. 5 (B) 

 (1894) 81-; 6 (B) (1895) 41-, 73-; Fschr. 

 Mth. (1893-94) 241. 



Approximations and series. Houzeau, J. C. 

 Brux. Ac. Bll. 41 (1876) 961-. 



Binomial Theorem 3220 



Asymptotic values of certain series. Le Roy, E. 

 Bll. Sc. Mth. 24 (1900) 245-. 



, infinite approximations, and order of 

 infinity in solution of equations. Du Boia- 

 Reymond, P. Mth. A. 8 (1875) 363-, 

 574-. 



Bernoulli's functions. Baraniecki, M. A. 



Krk. Ak. (Mt.-Prz.) Kz. 13 (1886) 183- ; 



Fschr. Mth. (1885) 416. 

 Binet's series, and products of a large number 



of factors. Gilbert, P. Brux. S. Sc. A. 10 



(1886) (Pt. 2) 191-. 



Binomial theorem. 



Ampere, A. M. Gergonne A. Mth. 15 (1824-25) 



369-. 

 Burg, A. Crelle J. 1 (1826) 367-; Wien Jb. 



Pol. I. 16 (1830) 171-. 

 De Morgan, A. Camb. Mth. J. 3 (1843) 



61-. 

 Barfuss, F. W. Grunert Arch. 5 (1844) 155- ; 



7 (1846) 3-; 8 (1846) 387-. 

 (Barfuss.) Schlomilch, O. Grunert Arch. 5 



(1844) 437-; 10 (1847) 321-. 

 Bianchi, G. [1844] Mod. Mm. S. It. 23 (1846) 



239-. 



Terquem, O. N. A. Mth. 9 (1850) 459-. I'"_ 

 Heine, H. E. Crelle J. 55 (1858) 279-. 

 Hinricks, G. Mth. Ts. 2 (1860) 38-. 

 Janni, V. G. Mt. 12 (1874) 229-, 312. 

 Lanza, G. Des Moines Anal. 1 (1874) 177-. 

 Gohierre de Longchamps, . N. A. Mth. 17 



(1878) 101-. 

 applications. Ferroni, P. [1801] Mod. S. It. 



Mm. 9 (1802) 291-. 

 demonstrations. Little, J. [1810] Ir. Ac. T. 



12 (1815) 31-. 

 . Knight, T. Phil. Trans. (1816) 331- ; 



(1817) 245-. 

 . Herapath, J. Thomson A. Ph. 13 (1819) 



365-. 



(Herapath). Ward, L. T. Tilloch Ph. Mg. 

 65 (1825) 432. 



. Colburn, W. Bost. J. Ph. 2 (1825) 



474-. 



. Strong, T. Silliman J. 12 (1827) 132-. 

 . Crelle, A. L. Crelle J. 4 (1829) 305- ; 



5 (1830) 187-. 

 . Cerquero, J. S. Quetelet Cor. Mth. 10 



(1838) 202-. 

 . Roche, . N. A. Mth. 1 (1842) 42-, 



118-. 

 . Cox, H. Camb. and Dubl. Mth. J. 7 



(1852) 98-. 

 . Paque, A. Liege Mm. S. Sc. 10 (1855) 



1-. 

 . Macnie, J. Des Moines Anal. 7 (1880) 



190-. 

 , direct. Gould, D. Silliman J. 19 (1831) 



50-. 



by fluxions. Evans, L. Tilloch Ph. Mg. 64 

 (1824) 270-. 



and generalisation. Eisenstein, G. Crelle 

 J. 28 (1844) 44-; N. A. Mth. 8 (1849) 

 344-. 



expansion. .Andre, D. N. A. Mth. 10 (1871) 

 74-. 



