3220 Expansion 



Infinite Series 



Expansion 3220 



Appell's polynomials. Pincherle, S. Em. E. 

 Ac. Line. Ed. 2 (1886) (Sem. 2) 214-. 



application of logarithmic method and of suc- 

 cessive approximations. Cauchy, A. L. C. 

 E. 19 (1844) 51-, 699-. 



method of successive approximations. 

 Bugaev, N. V. [1895] Eec. Mth. (Moscou) 

 18 (1896) 471- ; Fschr. Mth. (1896) 70, 71. 



approximate. Hoppe, R. Arch. Mth. Ps. 68 

 (1882) 37-. 



value of coefficients of higher order. Feraud, 

 A. Bordeaux Obs. A. 7 (1897) (Pt. 1) 37-. 



in ascending power-series. Collins, E. [1830] 



St Pet. Ac. Sc. Mm. 1 (1831) 475-. 

 . Grunert, J. A. Grunert Arch. 1 



(1841) 364-. 

 . Schlomilch, O. Grunert Arch. 7 



(1846) 353-. 

 . Bjorling, E. G. Stockh. Ak. 



Hndl. (1852) 165-. 

 powers of an increment, conditions. Fer- 



gola, E. Nap. Ac. Sc. Mm. 2 (1855-57) 197-. 

 cases. Noel, J. N. Quetelet Cor. Mth. 10 



(1838) 20-. 



. Schlomilch, O. Grunert Arch. 4 (1844) 



431- ; Schlomilch Z. 2 (1857) 420-. 

 . Dienger,J. Grunert Arch. 31 (1858) 274-. 

 . Vachette, A. N. A. Mth. 20 (1861) 155-. 

 . Walton, W. [1868] QJ. Mth. 10 (1870) 



. Catalan, E. C. N. A. Mth. 9 (1870) 199-. 

 . Dobinski, G. [1877] Arch. Mth. Ps. 63 



(1879) 108-. 



. Picard, E. C. E. 88 (1879) 167-. 

 . Marchand, J. N. A. Mth. 1 (1882) 450-. 

 . Bucca, F. Palermo Cir. Mt. Ed. 12 (1898) 



260-. 

 Cauchy's formula for expansion of function in 



powers of variable. Wantzel, L. Par. S. 



Phlm. PV. (1847) 15-. 

 class. Darboux, G. C. E. 82 (1876) 365-, 



404- ; Liouv. J. Mth. 4 (1878) 5-, 377-. 

 in continued fractions, functions arising from. 



Markov, A. [1893] St Pet. Ac. Sc. Mm. 



(Es.) 74 (1894) (Suppl.) No. 2, 30pp. ; Fschr. 



Mth. (1893-94) 330. 

 of continuous functions. Sonine, N. J. Mth. 



A. 16 (1880) 1-. 



Eisenstein's relation for coefficients in poly- 

 nomial expansion, proof. Moreno, G. G. 



Mt. 16 (1878) 174-. 



elementary expansion. Davies, T. S. Mathe- 

 matician 1 (1845) 5-. 

 formula, general. Ecfwls, W. H. N. Y. Mth. 



S. Bll. 2 (1893) 135-. 

 formulas. Cauchy, A. L. C. E. 19 (1844) 



1194-, 1331-. 



. Trudi, N. Nap. Ed. 1 (1862) 135-. 

 of four functions. Meyer, A. Brux. Ac. Sc. 



Mm. 21 (1848) 23 pp. 



function of binomial. [Greatheed, S. S. 

 non Gregory, D. F.l ff. Camb. Mth. J. 1 



(1839) 67-. 



functions of multinomials. Knight, T. 

 [1810] Phil. Trans. (1811) 49-. 



one variable. Jouvin, . Gard Mm. 



Ac. (1852-53) 381-. 



of functions of one variable. Eodier de la 

 Bruguiere, . Gard Mm. Ac. (1852-53) 

 394-. 



. Tchebicheff,P. [1859] St P(5t. 



Ac. Sc. Bll. 1 (1860) 193-. 



. Darboux, G. Liouv. J. Mth. 2 



(1876) 291-. 



. Halphen,G.H. Bll. Sc. Mth. 



As. 5 (1881) 462- ; C. E. 95 (1882) 629-. 

 two variables. Hermite, C. Crelle J. 



64 (1865) 294-. 

 . Renshaw, A. Mess. Mth. 3 



(1866) 225-. 

 several variables. Hermite, C. C. E. 



60 (1865) 370-, 432-, 461-, 512-. 

 very small variables. Caldarera, F. 



G. Mt. 12 (1874) 348-. 

 general coefficient. Andre, D. C. E. 85 (1877) 



786-. 

 . Anglin, A. H. H. Mess. Mth. 12 (1883) 



187-. 

 Hermite's method. Bering, . [1864] (x) 



Chemnitz B. 1 (1865) 23-. 

 Hoene-Wronski law. Dickstein, S. Prace Mt.- 



Fiz. 2 (1890) 145- ; 5 (1894 123- ; Fschr. 



Mth. (1890) 43; (1893-94) 394-. 

 of implicit functions. Cauchy, A. L. C. E. 9 



(1839) 587-. 

 . Bellavitis, G. [1879] Em. E. Ac. 



Line. Mm. 5 (1880) 43-. 

 . Gomes Teixeira, F. Liouv. J. Mth. 



7 (1881) 277-. 

 , application to Wronski's problem. 



Bassani, A. G. Teix. J. Sc. 10 (1891) 81-. 



intermediary function. Halphen, G. H. 

 Par. S. Mth. Bll. 7 (1879) 92-. 



irrationals of second degree and their Na- 

 pierian logs. Lucas, E. Par. S. Mth. Bll. 5 



(1877) 178-. 



in limited series. Cauchy, A. L. C. B. 34 



(1852) 8-, 70-, 121-. 

 method. Buquoy, G. von. Oken Isis (1826) 



244-. 



shortening astronomical calculations. 

 Cauchy, A. L. C. E. 19 (1844) 1122-. 



in periodic series. Cauchy, A. L. [1826] Par. 



Mm. Ac. Sc. 6 (1823) 603-. 

 of periodic series (Le Verrier). Encke, J. F. 



Berl. As. Jb. (1860) 313-. 



polynomial functions. Poselger, F. T. Berl. 

 Ab. (1828) 33-. 



in power series. Cauchy, A. L. C. E. 17 (1843) 



193-, 940- ; 19 (1844) 205- ; Liouv. J. Mth. 



11 (1846) 313-. 

 . Appell, P. Par. S. Mth. Bll. 11 



(1883) 65-. 

 principle, general. Schlomilch, 0. Schlomilch 



Z. 2 (1857) 289-. 

 of rational functions. Mittag-Leffler, G. 



Helsingf. Acta 11 (1880) 273-. 



. Faa de-Bruno, F. Am. J. Mth. 5 



(1882) 238-. 



real functions by method of least squares. 

 Gram, J. P. [1881] Crelle J. Mth. 94 (1883) 

 41-. 



and reversion of series. Frangais, J. F. Ger- 

 gonne A. Mth. 6 (1815-16) 61-. 



243 



