3220 Infinite Series 



Divergent series. Chessin, A. S. [1895] N. Y. 



Am. Mth. S. Bll. 2 (1896) 72-, 177-. 

 . Borel, E. Par. EC. Norm. A. 16 (1899) 



9-. 

 (Borel's formulae). Kluyver,J.C. Amst. 



Ak. Vs. 8 (1900) 331- ; Amst. Ak. P. 2 (1900) 



302-. 

 . Servant, M. Toul. Fac. Sc. A. 1 (1899) 



117-. 

 . Le Roy, E, C. B. 130 (1900) 1293-, 



1535-. 

 , comparison. Cesdro, E. Em. B. Ac. 



Line. Bd. 4 (1888) (Sem. 1) 115-. 



, discontinuity of arbitrary constants. 

 Stokes, G. G. [1857-68] Ph. Mg. 16 (1858) 

 71-; Camb. Ph. S. T. 10 (1864) 105- ; 11 

 (Pt. 2) (1869) 412-. 



and errors connected therewith. Young, 



J. E. IT. Ac. P. 3 (1847) 27-. 

 functions defined by Taylor's series. 



Le Roy, E. C. B. 127 (1898) 654-; 128 



(1899) 492-; Toul. Fac. Sc. A. 2 (1900) 

 317-. 



, legitimate use. Cauchy, A. L. C. E. 



17 (1843) 370-. 

 with positive terms. Appell, P. Arch. 



Mth. Ps. 64 (1879) 387-. 



, possibility of defining function by. 

 Pade, H. C. E. 116 (1893) 686-. 



, significance, values, etc. Prehn, . 



Crelle J. 41 (1851) 1-, 364-. 

 , sums. Hoppe, R. [1867] Ups. N. Acta 



S. Sc. 6 (1868) No. 7, 12 pp. 



summable series. Oldenburg, H. [1897] 

 Stockh. Ofv. (1898) 157-. 



, extension of Abel's theorem to, and 



generalisation of notion of limit. Borel, E. 

 C. B. 122 (1896) 73-. 



, theory, applications. Borel, E. C. 



B. 122 (1896) 805-. 



, , bases. Borel, E. Liouv. J. Mth. 



2 (1896) 103-. 

 Division. Hagen, J. Am. J. Mth. 5 (1882) 



236-. 

 Double series. Laurent, [Hermann non] Henry. 



C. E. 63 (1866) 296-. 



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



426-. 



. Stolz, 0. Mth. A. 24 (1884) 157-. 



, case. Catalan, E. C. Brux. Ac. Bll. 5 



(1883) 709-. 



, elementary theory. Pringsheim, A. 

 Munch. Ak. Sb. 27 (1898) 101-. 



of Kronecker's. Lerch, M. Prag Sb. 



(1893) (Mth.-Nt.) No. 9, 17 pp. 

 and products. Biermann, 0. Mh. Mth. 



Ps. 8 (1897) 115-. 

 sequences. London, F. Mth. A. 53 



(1900) 322-. 



Doubly-infinite converging series. Forsyth, 



A. R. QJ. Mth. 21 (1886) 261-. 

 sequences of numbers. Pringsheim, A. 



Mth. A. 53 (1900) 289-. 

 series, case. Cayley, A. Camb. and 



Dubl. Mth. J. 6 (1851) 45-. 

 , transformation. Brioschi, F. Torto- 



lini A. 7 (1856) 214-. 



Expansion 3220 



Elementary series. Igel, B. [1876] Wien Ak. 

 Sb. 74 (1877) (Ab. 2) 189-. 



, theory deduced from principle of inde- 

 terminate coefficients. Oliveira, G. B. Bv. 

 Brazil. 3 (1860) 194-. 



E qualities between series . Du Bois-Reymond , P. 

 Mth. A. 10 (1876) 576-. 



Equivalence. Catalan, E. C. Liege S. Sc. 

 Mm. 15 (1888) No. 1, 23-. 



Euler's series, square of. Glaisher, J. W. L. 

 [1889] L. Mth. S. P. 21 (1891) 182-. 



Expansion. 



Burja, . Berl. Mm. Ac. (1801) 3-. 



Sarrus, F. Gergonne A. Mth. 12 (1821-22) 



289-. 



Cauchy, A. L. Par. S. Phlm. Bll. (1822) 49-. 

 Paoli, P. Mod. S. It. Mm. 20 (1828) 293-. 

 Collins, E. [1828-31] St Pet. Ac. Sc. Mm. 2 



(1833) 19-, 195-. 



Crelle, A. L. Berl. Ab. (1830) 29-. 

 Cauchy, A. L. Ferussac Bll. Sc. Mth. 16 



(1831) 119-. 



Conti, C. A. Sc. Lomb. Yen. 1 (1831) 257-. 

 Gordon, J. Ph. Mg. 9 (1831) 253-. 

 Liouville, J. Liouv. J. Mth. 3 (1838) 561-. 

 Cauchy, A. L. C. B. 13 (1841) 909-. 

 Dienger, J. Grunert Arch. 7 (1846) 430- ; 8 



(1846) 450-. 



Brassinne, E. Toul. Mm. Ac. 2 (1852) 300-. 

 Faa de Bruno, F. Tortolini A. 6 (1855) 479-. 

 Friesach, K. Wien SB. 47 (Ab. 2) (1863) 



264-. 



Hermite, C. C. B. 58 (1864) 93-, 266-. 

 Sonln, N. Y. (xn) Bee. Mth. (Moscou) 5 



(1870) (Pt. 1) 271-, 323-. 



Kdnig, J. [1871] Mth. A. 5 (1872) 310-. 

 Lucas, E. [1877] Par. S. Mth. Bll. 6 (1878) 



57-. 



Faa de Bruno, F. Am. J. Mth. 3 (1880) 154-. 

 Hudson, E. C. QJ. Mth. 24 (1890) 233-. 

 Sochocki, J. Prace Mt.-Fiz. 2 (1890) 1-; Fschr. 



Mth. (1890) 260-. 



Echols, W. H. Am. J. Mth. 15 (1893) 316-. 

 by aid of Bernoulli's numbers. Thoman, F. 



C. B. 64 (1867) 655-. 

 differentiation. Cerquero, J. S. Cadiz 



Period. M. Ci. 1 (1848) 35-, 116-. 

 of algebraic functions. Eisenstein, G. Berl. 



B. (1852) 441-. 

 (Eisenstein). Heine, H. E. Crelle 



J. 45 (1853) 285-. 

 . Hamburger, M. Z. Mth. Ps. 16 



(1871) 461-. 



. David, (Lt.-Col.) . C. E. 89 



(1879) 219-. 

 . Rodrigues, J. M. As. Fr. C. B. 



(1893) (Pt. 2) 293-. 

 analytic functions. Tadini, A. Mil. G. S. 



Inc. 7 (1809) 63-; 8 (1809) 286-. 

 . Pincherle, S. Bologna Ac. Sc. Mm. 3 



(1881) 151- ; Mil. I. Lomb. Ed. 15 (1882) 224-. 

 analytic researches. Sarrus, F. Gergonne A. 



Mth. 10 (1819-20) 245-. 



of any power of polynomial, general term. Ger- 

 gonne, J. D. Gergonne A. Mth. 2 (1811-12) 



197-. 



242 



