3240 Lagrange's Series 



Indeterminate algebraic expressions. Studnicka, 



F. J. fiasopis 22 (1893) 321- ; Fschr. Mth. 



(1893-94) 464. 

 Jacobian of functions, extension of theory. 



Games Teixeira, F. Mh. Mth. Ps. 1 (1890) 



481-. 



Lagrange's Series. 



Cayley, A. Camb. Mth. J. 3 (1843) 283-. 

 Menabrea, L. F. [1843] Tor. Mm. Ac. 8 (1846) 



91-. 



Caraffa, A. Palomba Kac. 1 (1845) 43-. 

 Chio, F. [1846] Par. Mm. Sav. Etr. 12 (1854) 



340-. 



Dienger, J. [1847] Crelle J. 42 (1852) 287-. 

 Cayley, A. Camb. and Dubl. Mth. J. 6 (1851) 



37-. 

 Cauchy, A. L. C. E. 34 (1852) 309-, 316-, 



345-. 



Heine, H. E. Crelle J. 54 (1857) 388. 

 Tchebicheff, P. St Pet. Ac. Sc. Bll. 15 (1857) 



289-. 

 Oliveira, C. B. de. [1860] Ev. Brazil. 4 (1861) 



Rouche,E. [1861] C. E. 52 (1861) 295-; Par. 



Mm. Sav. Etr. 18 (1868) 457-. 

 (Eouche.) Bertrand,J. C. E. 52 (1861) 1301-. 

 Laurent, [Herm. non] Henry. C. E. 60 (1865) 



25-. 



Chio, F. Tor. At. Ac. Sc. 7 (1871-72) 647-. 

 Zolotarev, E. I. N. A. Mth. 15 (1876) 422-. 

 Rodrigues, J. M. G. Teix. J. Sc. 4 (1883) 



121- ; 8 (1887)59-. 



Hamy, M. Bll. Sc. Mth. 20 (1896) 213-. 

 analogue. Cauchy, A. L. [1824] Par. Mm. 



Ac. Sc. 9 (1830) 104-. 

 approximate determination of mth term where 



m is very great. Nekrasov, P. A. [1900] 



Eec. Mth. (Moscou) 21 (1901) 439-; Fschr. 



Mth. (1900) 268. 

 and approximate expressions for functions of 



large numbers. Nekrasov, P. A. Eec. Mth. 



(Moscou) 12 (1885) 49-, 315-, 432, 483-, 



643-; Fschr. Mth. (1885) 212-. 



Burmann's series. Dienger, J. [1868] Prag 

 Ab. 3 (1870) 25 pp. 



controversy. Genocchi, A. Tor. At. Ac. Sc. 

 8 (1872-73) 18-. 



convergence, Cauchy's and Lagrange's con- 

 ditions. Menabrea, L. F. C. E. 77 (1873) 

 1358-. 



, (Menabrea). Genocchi, A. C. 



E. 77 (1873) 1541-. 



demonstration. Miller, T.H. Edinb. Mth. S. P. 

 4 (1886) 45-. 



and forms, new. Meech, L. W. Des 

 Moines Anal. 3 (1876) 33-. 



demonstrations, three. Rothe, H. A. Kastner 



Arch. Ntl. 12 (1827) 1-. 

 expansion derived from. Glaisher, J. W. L. 



[1877] Mess. Mth. 7 (1878) 118-. 

 extension. Peirce, B. Gould As. J. 5 (1858) 



164. 

 generalisation. Moth, F. X. Baumgartner Z. 



7 (1830) 64-. 



Other Series 3240 



generalisation. Gomes Teixeira, F. [1876-79] 



Lisb. J. Sc. Mth. 5 (1876) 203- ; 7 (1880) 247-. 

 . Cesdro, E. N. A. Mth. 4 (1885) 316-. 

 . Stieltjes, T. J. Par. EC. Norm. A. 2 (1885) 



93-. 



. Bassani, A. Yen. I. At. (1886-87) 1163-. 

 .Laplace's. Schlfijli,L. QJ. Mth. 2 (1858) 24-. 

 requiring proof. Schlafli, L. Bern Mt. 



(1848) 97-. 

 interpretation. Menabre'a, L. F. [1846] Tor. 



Mm. Ac. 10 (1849) 111-. 

 Lagrange-Cauchy formula. Zinin, N. N. 



Vars. S. Nt. Tr. (1897) (Ps. C.) Fasc. 2, No. 6. 

 remainder. Ramus, C. Kiob. Dn. Yd. Selsk. 



Afh. 9 (1842) 365-. 



. Popoff, A. C. E. 53 (1861) 795-. 

 successive differentiations connected with. 



Knar, I. Baumgartner Z. 3 (1827) 175-. 

 summation by definite integrals. Parseval, 



M. A. [1804] Par. Mm. Sav. Etr. 1 (1806) 



567-. 

 . Gruson,J.P. Berl. Ab. (1812-13) 



(Mth.) 31-. 

 and summation of series. Dienger, J. Crelle 



J. 34 (1847) 75-. 

 symbolic theorems derived from. Glaisher, 



J. W. L. QJ. Mth. 16 (1879) 263-. 



Laplace's series. Mainardi, G. Em. At. N. 



Line. 20 (1867) 164-. 



. Darboux, G. C. E. 68 (1869) 324-. 



. Saint-Germain, A. L. de (xn) Caen 



Ac. Mm. (1880) 112-. 



, remainder. McClintock, E. Am. J. 

 Mth. 4 (1881) 96. 



, summation. Dirksen, E. H. Berl. Ab. 



(1839) (Mth.) 49-. 

 Maclaurin's series. Adams, Jas. Thomson 



A. Ph. 1 (1821) 98-. 

 . Hermite, C. [1877] Crelle J. Mth. 



84 (1878) 64-. 



. Genocchi, A. C. E. 86 (1878) 466-. 



. Callandreau, O. C. E. 86 (1878) 589-; 



Par. S. Mth. Bll. 15 (1887) 23-. 

 .convergence. Timmermans, J. A. Brux. 



Ac. Bll. 13 (1846) 53-. 



, demonstration, direct. Dienger, J, 

 Grunert Arch. 12 (1849) 93-; 13 (1849) 333-. 



, legitimate use. Jacobi, C. G. J. Crelle 



J. 12 (1834) 263-. 

 , limits. Craufurd, A.Q.G. Camb. Mth. 



J. 3 (1843) 84-, 159-. 

 for real variable. Callandreau, 0. C. E. 



104 (1887) 38-. 

 , and application to potential of a 



homogeneous body. Callandreau, 0. C. E. 



103 (1886) 864-, 954. 

 , symbolic form, applications. Walton, W. 



Camb. Mth. J. 4 (1845) 176-. 

 , theory. Scheibner, W. Leip.B. 9 (1857) 



190-. 



theorem, demonstration. Hayes, J. S. 

 Des Moines Anal. 8 (1881) 149-; 9 (1882) 12-. 



, expansion of circular functions by. 

 Rutherford, W. Mathematician 3 (1850) 35-. 



, remainder. Veneziani, C. Am. J. Mth. 



7 (1885) 168-. 



261 



