3240 



Application of the Differential Calculus 



3240 



Arbogast's method of derivations, extension. 



Thomson, J. J. Mess. Mth. 7 (1878) 142-. 

 , (Cayley). Jenkins, M. Am. 



J. Mth. 10 (1888) 29-. 

 , explained by combinations. De Morgan, 



A. Camb. and Dubl. Mth. J. 6 (1851) 35-. 



theory of separation of symbols of operation. 

 Harvey, G. Thomson A. Ph. 16 (1820) 178-. 



Building and restoration expenses, mathe- 

 matical theory. Launhardt, . Hann. 

 Archt.-Vr. Z. 33 (1887) 367-. 



Calculation of function from its derivatives. 

 Riquier, C. Mars. Fae. Sc. A. 10 (1900) 

 (Fasc. 1) 60 pp. 



Coefficient of general term in certain expansions. 

 Anglin, A. H. Par. S. Mth. Bll. 15 (1887) 

 192-. 



Derivatives of composite functions, combina- 

 torial representation. Vollers, J. Arch. 

 Mth. Ps. 1 (1884) 64-. 



function of function, application to 

 Bernoulli's numbers. Presle, de. Par. 

 S. Mth. Bll. 16 (1888) 157-. 



, higher, algebraic relations between co- 

 efficients. Meyer, F. Mth. A. 36 (1890) 453-. 



of sec x. Stieltjes,. C. B. 108 (1889) 605-. 

 Differential calculus, theorem. Hobson, E. W. 



Mess. Mth. 23 (1894) 115-. 



coefficients compared with Bernoulli's num- 

 bers. Eytelwein,J.A. Berl. Ab. (1816-17) 28-. 



Differentiation of certain infinite expressions. 



Kretkowski, W. Fschr. Mth. (1888) 280. 

 Eisenstein's theorem. Gomes Teixeira, F. 



Par. EC. Norm. A. 3 (1886) 389-. 

 Euler-McLaurin summation formula and its 



applications. Pokrovsky, P. M. Fschr. Mth. 



(1898) 216. 

 Expansion coefficients of (l-a;)*log p (1 -x). 



Feraud, A. Bordeaux S. Sc. PV. (1896- 



97) 93-. 



of Didon's, an. Escary, . C. B. 86 

 (1878) 1014-. 



explicit algebraic functions in series, 

 mode. Mangeot, S. Par. EC. Norm. A. 14 

 (1897) 247-. 



function. Echols, W. H. A. Mth. 



8 (1893-94) 176-. 



in given interval, according to 

 mean values. Leaute, H. Liouv. J. Mth. 

 7 (1881) 185-. 



functions. Corey, S. A. A. Mth. 1 



(1900) 77-.^ 

 , application of method of least squares. 



Gilman, F. Franklin I. J. 137 (1894) 438-. 

 of form F(z + x). Roberts, S. Ph. 



Mg. 32 (1848) 284-. 

 functions, theorem. McClintock, E. 



Am. J. Mth. 2 (1879) 348-; 3 (1880) 173. 

 , particularly integrals, new formula. 



Lagrange, C. Brux. Ac. Bll. 9 (1885) 114-. 



in power series of determinant. 

 Capelli, A. Palermo Cir. Mt. Ed. 1 (1887) 

 58, 133-. 



sines and cosines. Gomes 



Teixeira, F. Bll. Sc. Mth. 14 (1890) 200- ; 

 G. Teix. J. Sc. 10 (1891) 35-; Crelle J. Mth. 

 116 (1896) 14-. 



260 



Expansion of functions in series. Gomes 



Teixeira, F. Madrid Ac. Ci. Mm. 18 (Pt. 1) 



(1897) 116 pp. 

 of several variables by McLaurin's 



series. PtaSickij, I. L. Kharkov Mth. S. 



Com. (1884) 73-; Fschr. Mth. (1885) 211. 

 , general form. Hill, C. J. D. Lund Acta 



Un. 6 (1869) (Mth.) No. 1, 36 pp. 



of implicit functions. David, . Par. EC. 

 Pol. J. 57 (1887) 147-. 



. Gomes Teixeira, F. Liouv. J. 



Mth. 5 (1889) 67-. 



in series. Worontzoff, . N. A. 



Mth. 13 (1894) 167-. 



Leaute 's polynomials in trigonometric 



series. Appell, P. N. A. Mth. 16 (1897) 

 265-. 



/ (x) , f (x, y) , etc. Adams, Jas. Thom- 

 son A. Ph. 1 (1821) 359-. 



f(z) in ascending powers of h, when 

 z - x - hir (z) = 0. Cauchy, A. L. Par. Mm. 

 Ac. Sc. 8 (1829) 130-. 



F (x + h). Powers, , <& Pike, . [1841] 



Am. Ph. S. T. 8 (1843) 155-. 



f(z, z 1 ) in ascending powers oty,y' where 



z=x + yf(z). Raabe, J. L. Zur. Mt. 1 

 (Heft 2) (1847-48) 36-; Crelle J. 48 (1854) 



F(x + h). Whitcom, A. W. Am. J. Mth. 



3 (1880) 344-. 

 e-W-*), with applications. Saalschiltz, L. 



Arch. Mth. Ps. 6 (1888) 305-, vii. 

 Expansions of rational functions in series. 



Biehler, C. N. A. Mth. 6 (1887) 485-. 

 , theory. Boole, G. Camb. Math. J. 4 (1845) 



214-. 



Explicit representation of J^ (x - a)? (x - b). 



Oppermann, L. H. F. (xn) Ts. Mth. 5 (1881) 



184-. 

 Factorial derived functions. Laisant, A. As. 



Fr. C. E. (1898) (Pt. 2) 76-. 

 Finite difference formula. D g. Ts. Mt. 



Fys. 2 (1869) 215-. 

 Forestry, felling periods. Dienger, J. Arch. 



Mth. Ps. 41 (1864) 191-. 

 Formula including binomial theorem. Abel, 



N. H. Crelle J. 1 (1826) 159-. 

 . Gerono, G. C. N. A. Mth. 16 



(1857) 237-, 398-. 



n F (nx) =f (x) +f ( x + - J + etc. Kinkelin, 



H. Grunert Arch. 22 (1853) 189-. 

 Formulae, general. Libri, G. Crelle J. 7 



(1831) 57-. 

 Function of functions, nth differential. Arez, 



J. G. Teix. J. Sc. 12 (1895) 110- ; Fschr. 



Mth. (1895) 307-. 

 "Functionesinexplicabiles," i.e. not expansible 



by Taylor's theorem. Euler, L. [1780] St 



Pet. Ac. Sc. Mm. 4 (1813) 88-. 

 Functions, analytical, abrupt changes of value. 



Du Bois-Reymond, P. [1873] (vn) Mth. 



A. 7 (1874) 241-. 

 General theorems, two, including Lagrange's 



and Laplace's. Johnson, A. R. Mess. Mth. 



14 (1885) 76-. 



