3220 Infinite Series 



Binomial Theorem, continued. 



expansion. Kluyver, J. C. Amst. Ak. Vs. 6 



(1898) 421-. 

 , approximate formulas. Astrand, J. J. 



Grunert Arch. 12 (1849) 420-. 

 , properties derivable from. Young, J. E. 



Ph. Mg. 33 (1848) 268-. 

 expression in form of a factorial which is 



always convergent. Kummell, C. H. A. 



Mth. 12 (1898-99) 60-. 

 fractional index, demonstration. Robertson, A. 



Phil. Trans. (1806) 305-. 



or negative index, demonstration. Anon. 

 (vi 1170) Thomson A. Ph. 7 (1816) 346-. 



, . Eodrigues, O. Liouv. J. 

 Mth. 3 (1838) 550-. 



, Euler's demonstration. Muirhead, 



E. F. Edinb. Mth. S. P. 17 (1899) 38-. 



, extension. Davidov, A. Y. (xn) 



Eec. Mth. (Moscou) 3 (1868) (Pt. 2) 1-. 



, historical note. Terquem, 0. 

 N. A. Mth. 6 (1847) 85-. 



generalised, expansion of factorial by. Cayley, 



A. Ph. Mg. 6 (1853) 182- ; Mess. Mth. 5 



(1871) 102-. 

 geometrical treatment. Koppe, M. Arch. Mth. 



Ps. 61 (1877) 113-. 

 and logarithmic theorem. Catlin, M. Mth. 



Misc. 1 (1838) 113-. 

 methods of demonstration. Davies, T. S. 



Tilloch Ph. Mg. 66 (1825) 115-. 

 negative index, demonstration. Trowbridge, D. 



Des Moines Anal. 2 (1875) 71-. 



integral index, demonstration. Grunert, 

 J. A. Grunert Arch. 30 (1858) 336-. 



particular case. Catalan, E. C. C. E. 45 



(1857) 641-. 

 series analogous to binomial series. Jacobi, 



C. G. J. Crelle J. 32 (1846) 197-. 

 , two groups. Weiss, E. Wien 



Ak. Sb. 91 (1885) (Ab. 2) 587-. 



Calculation of series. Poncelet, J. V. [1833] 



Par. Mm. Sav. Etr. 6 (1835) 641-. 

 Class. Schlomilch, O. Schlomilch Z. 1 (1856) 



21-. 

 Classification. Chessin, A. S. J. H. Un. Cir. 



[15 (1895-96)] 39. 

 Coefficients in a certain series. Bfdrling, E. G. 



Crelle J. 28 (1844) 284-. 



, especially factorial coefficients, determina- 

 tion. SchlSmilch, 0. Grunert Arch. 18 



(1852) 306-. 

 Conditionally convergent series. Schlomilch, 0. 



Leip. B. 24 (1872) 327-. 

 , multiplication. Pringsheim, A. 



Mth. A. 21 (1883) 327-. 

 : , . Voss, A. Mth. A. 24 (1884) 



42-. 

 and products. Pringsheim, A. Mth. 



A. 22 (1883) 455-. 

 Continued identity, method. Kummell, C. H. 



A. Mth. 5 (1889-90) 85-, iv. 

 Continuity of sums, theorem of Cauchy. I>u 



Bois-Reymond, P. Mth. A. 4 (1871) 135-. 

 . , two theorems of Abel. Pringsheim, 



A. Munch. Ak. Sb. 27 (1898) 343-. 



Convergence 3220 



Convergence. 



Olivier, L. Crelle J. 2 (1827) 31-. 



(Olivier.) Abel, N. H. Crelle J. 3 (1828) 



79-. 

 Cauchy, A. L. G. E. 9 (1839) 587-; 10 (1840) 



640- ; 11 (1840) 639-, 667-. 

 Binet, 'J. P. M. Liouv. J. Mth. 6 (1841) 



495-. 



Cauchy, A. L. C. E. 19 (1844) 141-, 157. 

 Malmsten, C. J. Ups. N. Acta S. Sc. 12 (1844) 



255-. 

 Schulten, N. G. af (fil.) [1844] Helsingf. 



Acta 2 (1847) 733-. 

 Cauchy, A. L. C. E. 20 (1845) 126-. 

 Lebesgue, V. A. N. A. Mth. 4 (1845) 66-. 

 Malmsten, C. J. Grunert Arch. 8 (1846) 



419-. 



Terquem, 0. N. A. Mth. 5 (1846) 101-. 

 Timmermans, J. A. Brux. Ac. Bll. 13 (1846) 



140-. ' 

 Schaar, M. Brux. Mm. Cour. 4", 22 (1846-47) 



9 pp. 

 Schlomilch, 0. Grunert Arch. 14 (1850) 



105-. 

 Arndt, F. Grunert Arch. 20 (1853) 43-, 461- ; 



21 (1853) 78-. 



Kinkelin, H. Bern Mt. (1858) 57-. 

 Ermakof, V. Bll. Sc. Mth. As. 2 (1871) 250- ; 



7 (1883) 142-. 

 Petersen, J. P. C. (xn) Ts. Mth. 3 (1873) 



49-. 



Grolous, J. As. Fr. C. E. 6 (1877) 209-. 

 Kohn, G. Arch. Mth. Ps. 67 (1882) 63-. 

 Jensen, J. L. W. V. Ts. Mth. 2 (1884) 63- ; 



Fschr. Mth. (1884) 192-. 

 Mansion, P. Mathesis 5 (1885) 270-. 

 Bugaev, N. V. [1888] Eec. Mth. (Moscou) 14 



(1890) 279- ; Fschr. Mth. (1889) 232. 

 Cesdro, E. C. E. 106 (1888) 1142- ; N. A. 



Mth. 7 (1888) 49-, 190. 

 (Cesaro.) Jensen, J. L. W. V. C. E. 106 



(1888) 1520-. 

 Lerch, M. Prag Sb. (1890) 1 (Mth. Nt.) 



219-. 



Cohen, E. N. A. Mth. 10 (1891) 453-. 

 Gilbert, P. Brux. S. Sc. A. 15 (1891) (Pt. 1) 



69-. 

 Bryant, E. [1895] L. Mth. S. P. 27 (1896) 



69-. 

 Lerch, M. D. Nf. Vh. (1899) (Th. 2, Halfte 1) 



Sincov, D. M. Eec. Mth. (Moscou) 20 (1899) 



616- ; Fschr. Mth. (1899) 228. 

 and approximate value of functions of high 



numbers. Lobatschewsky , N, (vi Adds.) 



Kazan Mm. Un. (1835) (cah. 2) 211-. 

 characteristics. Andries, F. Brux. A. Un. 



(1846) 99-. 



. Doucet, . N. A. Mth. 8 (1869) 266-. 

 . Hadamard, . C. E. 117 (1893) 



844-. 

 for series with positive terms ; and functions 



increasing indefinitely. Hadamard , J, Acta 



Mth. 18 (1894) 319-, 421. 

 circle of convergence. Leau, . C. E. 127 



(1898) 711-, 794. 



239 



