3220 Convergence 



Infinite Series 



Convergence 3220 



circle of convergence, convergence and di- 

 vergence on. Thome, L. W. Crelle J. Mth. 

 100 (1887) 167-. 



for reverted series. Stolz, O. 



Ak. Sb. 104 (1895) (Ab. 2a) 485-. 



, singular points on, and summation of 



divergent series. Lean, . C. E. 127 (1898) 

 607-. 



condensation test, Cauchy's. Hill, M. J. M. 

 Mess. Mth. 26 (1897) 102-. 



conditions. Liouville, J. C. E. 11 (1840) 

 615-. 



. Dirksen, E. H. Berl. B. (1845) 349-. 



. Fouret, G. N. A. Mth. 9 (1890) 

 222-. 



(Fouret). Giudice, . Palermo Cir. Mt. 

 Ed. 4 (1890) 284-. 



. Giudice, . Palermo Cir. Mt. Ed. 4 



(1890) 275-, 276-, 278-, 279, 279-, 280-, 



281-, 283. 

 of continued fractions. Markov, A. St Pet. 



Ac. Sc. Mm. (Es.) 72 (1893) 8- ; Fschr. Mth. 



(1893-94) 329-. 

 criteria. Schulz von Strasznitzki, L. C. 



Baumgartner Z. 5 (1829) 10-. 

 . Schlomilch, 0. Z. Mth. Ps. 11 (1866) 



354-. 

 . Cajori, F. [1892] N. Y. Mth. S. Bll. 2 



(1893) 1-. 



. Saint-Germain, A. de. C. E. 115 (1892) 



1258-. 

 , Bertrand's, generalisation. Petrini, H. 



Stockh. Ofv. (1899) 691-. 

 , connection. Zahradnik, K. Casopis 7 



(*1878) 91-; Fschr. Mth. (*1878) 176. 



dating from beginning of eighteenth century. 

 Enestrim, G. Stockh. Ofv. 36 (1879) No. 9, 

 71-. 



, Gauss's. Hornstein, K. Prag Sb. (1864) 



52-. 

 , , simple proof. Pranghofer, J. Wien 



Sb. 53 (1866) (Ab. 2) 503-. 

 , general. Lerch, M. fiasopis 20 (1891) 



285-; Fschr. Mth. (1891) 248-. 

 , Eiemann's. Hurwitz, A. Mth. A. 44 



(1894) 83-. 



, , extension. Arzela, C. [1900] Bologna 



Ed. 5 (1901) 25-. 

 and divergence. Burg, A. Wien Jb. Pol. I. 



17 (1832) 112-. 

 . Raabe, J. L. Baumgartner Z. 10 (1832) 



41- ; Crelle-J. 11 (1834) 309-. 

 . Rummer, E. E. Crelle J. 13 (1835) 



171-. 

 . Bonnet, 0. [Bennet erroneously inC.S.P.] 



Liouv. J. Mth. 8 (1843) 73-. 

 . Schlomilch, O. Z. Mth. Ps. 10 (1865) 



. Aller, C. van. N. Arch. Wisk. 12 



(1886) 204-. 

 , conditions. Dirksen, E. H. Berl. Ab. 



(1832) 77-. 

 , criterion. Hoppe, B. Grunert Arch. 



26 (1856) 217-. 



, limiting regions and so-called limit. 

 Pringsheim, A. Munch. Ak. Sb. 26 (1897) 

 605-. l ' 



and divergence of series with positive terms. 



Du Bois-Reymond, P. C. E. 107 (1888) 



941-. 

 Wien . Pringsheim, A. Mth. A. 



35 (1890) 297- ; 39 (1891) 125-. 

 . Petrini, H. Stockh. 



Ofv. (1900) 895-. 



, limits. Thomae, J. 



[1871] A. Mt. 5 (1871-73) 121-. 



, new theory. Du Bois- 

 Reymond, P. [1872] Crelle J. 76 (1873) 61-. 



or divergence, simultaneous, of two series. 

 Schlomilch, O. Z. Mth. Ps. 18 (1873) 425-. 



of double series of Lame. Escary, . C. E. 

 88 (1879) 558-. 



in theory of heat. Escary, . As. Fr. 



C. E. (1886) (Pt. 2) 149- ; (1887) (Pt. 2) 

 1092. 



in finite difference and in differential series. 

 Crelle, A. L. [1839] Crelle J. 22 (1841) 

 249-. 



of hypergeometric series. Horn, J. Mth. A. 

 34 (1889) 544-. 



Lambert's series. Stolz, 0. Wien Ak. Sb. 95 

 (1887) (Ab. 2) 659-. 



limit of convergence, behaviour of infinite 

 series at. Lasker, E. [1900] Phil. Trans. 

 (A) 196 (1901) 431-. 



, Du Bois-Eeymond's, and a special 



form of conditions of convergence. Prings- 

 heim, A. Munch. Ak. Sb. 27 (1898) 303-, 

 356-. 



of series representing integrals of 

 differential equations. Picard, E. C. E. 

 106 (1888) 1466-. 



limits of convergence, theorem. Cauchy, A. L. 



C. E. 40 (1855) 162-. 

 of logarithmic series. Doppler, C. Wien Jb. 



Pol. I. 17 (1832) 172-. 



multiple series. Cauchy, A. L. C. E. 19 

 (1844) 1433-. 



, conditions. Jordan, C. Par. S. Mth. 



Bll. 9 (1881) 113-. 



Newton's binomial series for case x=l. 

 Broch, 0. J. As. Fr. C. E. 7 (1878) 145-. 



non-uniform. Chessin, A. S. Am. J. Mth. 18 



(1896) 128-. 

 , and integration of series term by term. 



Osgood, W. F. [1896] Am. J. Mth. 19 (1897) 



155. 

 regions of convergence. Dietrich, R. Arch. 



Mth. Ps. 69 (1883) 381-. 

 , continuity in. Meyer, A. (of Stock- 

 holm). Stockh. Ofv. 40 (1883) No. 9, 15-; 



Fschr. Mth. (1884) 203. 

 of reversions of series. Zorawski, K. Crc. Ac. 



Sc. Bll. (1899) 75-; Krk. Ak. (Mt.-Prz.) Ez. 



17 (1900) 139-. 

 rule. Duhamel, J. M. C. Liouv. J. Mth. 4 



(1839) 214-. 



. Genocchi, A. N. A. Mth. 6 (1867) 261-. 

 . , Gauss's, demonstration. Godefroy, . 



N. A. Mth. 18 (1899) 157-. 

 , , generalisation. Saint-Germain, A. de. 



Bll. Sc. Mth. 14 (1890) 212-. 

 , Eaabe's. Longchamps, G. de. N. A. Mth. 



19 (1900) 216-. 



240 



