3230 Principles and Elements of the Differential Calculus 3230 



Differentials, higher, of y =\ f a? - b 2 x 2 . Grunert, 



J. A. Grunert Arch. 3 (1843) 236-. 

 , , = , law of coefficients. Luchter- 



handt, A. R. Grunert Arch. 4 (1844) 87-. 

 , new method of finding. Wilson, W. D. 



Des Moines Anal. 1 (1874) 195-. 

 , proof for. Ficklin, J. [1883] Sid. Mess. 



2 (*1883-84) 209-. 

 , any order. Tardy, P. Tortolini A. 1 



(1858) 135-. 

 _;__. Rutgers, A. Arch. Neerl. 7 (1872) 



27-. 

 , . Gomes Teixeira, F. G. Mt. 18 



(1880) 301-. 



, , of certain general functions, theo- 

 rems. Schlomilch, O. Crelle J. 32 (1846) 1-. 

 , 2nd and higher orders. Miller, E. Kan. 



Ac. Sc. T. 12 (1890) 65-. 

 , successive, of a function of one variable, 



geometrical representation. Fontent, G. 



Ens. Mth. 1 (1899) 458-. 

 , , several variables. Moutard, 



. C. E. 124 (1897) 603-. 

 _,_,_. . Goursat, E. C. E. 



124 (1897) 676. 

 , , sum. Genocchi, A. Tortolini A. 8 



(1857) 289-. 

 , transformation. Jurgensen, C. Mth. Ts. 



2 (1860) 1-. 

 versus differential coefficients. Magistrini, 



G. B. [1846] Bologna Mm. Ac. Sc. 1 (1850) 



297-. 



, (l-z 2 ) n ~^. Liouville, J. Liouv. 



J. Math. 6 (1841) 69-. 

 , -^ JL (1 - 2 2 ) i-i . Grunert, J. A. Grunert 



Arch. 4 (1844) 104- . 

 Differentiation, application of factorials. Langs- 



dorf, W. Grunert Arch. 21 (1853) 249-. 

 , Fourier's formula. Liouville, J. 



Crelle J. 13 (1835) 219-. 

 , fundamental formulae to summation 



of infinite series. Florov, P. S. Kharkov 



Mth. S. Com. (1886) 3- ; Fschr. Mth. (1886) 



245. 

 , to periodic series. Young, J. R. Ph. 



Mg. 28 (1846) 213-. 



for values of y given by < (x, y)=0. Spitzer, 



S. Grunert' Arch. 25 (1855) 137-. 

 by finite differences and vice versa. Lobatto, 



R. Crelle J. 16 (1837) 11-. 

 , formula for. Cayley, A. E. S. P. 9 



(1857-59) 93- ; Tortolini A. 2 (1859) 214-. 

 .fractional. Greer.H.R. QJ. Mth. 3 (1860) 



327-. 

 , . Zachartchenxo, W. [Vashchenko- 



Zakharchenko, AT.] QJ. Mth. 4 (1861) 



, (Eiemann). Cayley, A. [1879] Mth. 



A. 16 (1880) 81-. 

 , , theory and application. Liouville, J. 



Par. EC. Pol. J. 21 cah. (1832) 1-. 



. . 



(Pt. 1) 1-, 

 (x) Bll. Sc. 



Differentiation of functions of functions. Anne, 



T. (vi Adds.) N. A. Mth. 9 (1850) 119- ; 



11 (1852) 376-. 

 . Gomes Teixeira, F. G. Teix. 



J. Sc. 7 (1886) 150- ; 9 (1889) 137- ; Fschr. 



Mth. (1885) 242- ; (1889) 261-. 

 , general. Greatheed, S. S. [ff.] Camb. 



Mth. J. 1 (1839) 11-, 109-. 

 , . Kelland, P. [1839] Edinb. E. S. T. 



14 (1840) 567-, 604- ; 16 (1849) 241-. 

 , . Hammond, J. Am. J. Mth. 3 (1880) 



164-. 

 _, _. Nekrasov, P. A. [1888] Eec. Mth. 



(Moscou) 14 (1890) 45- ; Fschr. Mth. (1888) 



275-. ' 

 , imaginaries in. Gilbert, P. Brux. Ac. 



Bll. 33 (1872) 108-. 



to any index. Liouville, J. Par. EC. Pol. 

 J. 21 cah. (1832) 71-. 



. Holmgren, H. [1865] Stockh. 



Ak. Hndl. 5 (1866) (No. 11) 83 pp. 

 . Sonln, N. Y. [1869] (xn) Eec. 



Mth. (Moscou) 6 (1872-73) (Pt. 1) 1-. 



, new method. Buchwaldt, F. 

 Kjob. Ov. (1876) 51-, 248 ; (Resume, 14-). 



. theory. Lyetnikov [Letnikovn, 



A. V. (xn) Eec. Mth. (Moscou) 3 (1868) 

 L-, 85- ; 6 (1872-73) (Pt. 1) 413- ; 

 Mth. As. 6 (1874) 316-. 



and integration. Gosiewski, W. Par. T. 

 Nauk S"c. Pam. 12 (*1882) Art. 3, 15 pp. 



, introduction to. Macnie, J. Des Moines 



Anal. 7 (1880) 152-. 

 , metaphysics. Nieuport, C. F. F. de. [1822] 



Brux. Ac. Sc. Mm. 2 (1822) 45-. 

 , method independent of expansion. Francois, 



J. F. Gergonne A. Mth. 2 (1811-12) 325-. 

 , multiple, of certain expression. Glaisher, 



J. W. L. Ph. Mg. 2 (1876) 208-, 522-. 

 , order indifferent, assumptions required for 



proof. Schwarz, H. A. Sch. Nf. Gs. Vh. 



66 (1873) 259-. 

 , , proofs. Lindelof, L. L. [1866] 



Helsingf. Acta 8 (1867) 205-. 



of a power. Schlomilch, 0. Grunert Arch. 

 10 (1847) 42-. 



, problem. Jacobi, C. G. J. Crelle J. 6 



(1830) 212. 

 , successive, of composite functions. Mossa, 



F. G. Mt. [13 (1875)] 175-. 

 , , formula. Scott, G. QJ. Mth. 4 (1861) 



77-. 



of symmetrical determinant, theorem. 

 Glaisher, J. W. L. [1876] QJ. Mth. 14 

 (1877) 245-. 



transcendental functions. Unger, E. S. 



Oken Isis (1825) 1162-. 

 unknown function, error to be avoided. 



Buquoy, G. von. Oken Isis (1824) 93-. 

 *. Matzka, W. Grunert Arch. 6 (1845) 



335-. 

 {/(*)}*. Getting, R. [1870] Mth. A. 



3 (1871) 276-. 

 Euler's theorem, proof. Orlov, T. E. [1866] 



(xn) Eec. Mth. (Moscou) 2 (1867) (Pt. 1) 321-. 

 Exponential calculus. Curten, P. Eot. N. 



Vh. 5 (1810) 59-. 



256 



