Logarithmic, Circular, Exponential Functions 



4030 



Compound interest and current accounts. 



Starkov, A. N. Es. S. Nt. Mm. (Mth.) 3 



(*1881). 

 Discontinuous logarithmic functions. Bugaev, 



N. V. [1887-88] Eec. Mth. (Moscou) 13 



(1886) 757-; 14 (1890) 1- ; Fschr. Mth. 



(1888) 186. 



4030 



Equations of form S 



F (z) dz 



Laguerre, E. C. B. 93 (1881) 1000-. 

 Expansion. Bangma, 0. S. Amst. Mengel- 



werk 2 (1816) 92-. 

 . Cerquero, J. S. Quetelet Cor. Mth. 10 



(1838) 383-. 



in convergent series. Oliveira, C. B. Bv. 

 Brazil. 3 (1860) 205-. 



series. Gergonne, J. D. Gergonne A. 



Mth. 5 (1814-15) 363-. 

 Exponential equations, reduction to algebraic 



form. Leyomnark, G. A. Stockh. Ak. 



Hndl. 29 (1808) 284-; 31 (1810) 101-. 

 , solution. Arnott, G. A. W. Tilloch 



Ph. Mg. 49 (1817) 321-. 



expressions, imaginary. Roy, A. Mathe- 

 matician 3 (1850) 13-. 



forms, indeterminate. Franklin, F. Am. 

 J. Mth. 1 (1878) 368-. 



functions. Hermite, C. C. E. 77 (1873) 

 18-, 74-, 226-, 285-. 



. Laguerre, E. [1879] Par. S. Mth. Bll. 



8 (1880) 11-. 



__. Gegenbauer, L. Wien Ak. Sb. 95 (1887) 

 (Ab. 2) 846- ; Mh. Mth. Ps. 5 (1894) 303-. 



, application, case. Hilgard, J. E. Am. 



As. P. 20 (1871) 61-. 

 , case. Pagani, G. M. Brux. Ac. Bll. 



13 (1846) (pte. 2) 347-. 

 , expansion in continued fractions. Pad, 



H. Par. EC. Norm. A. 16 (1899) 395-. 



, Lindemann's theorem. Vahlen, T. 

 Mth. A. 53 (1900) 457-. 



, periodicity. Studnicka, F. J. Casopis 



23 (1894) 1-; Fschr. Mth. (1893-94) 737. 



, representation by infinite product. 

 Lipschitz, E. C. E. 99 (1884) 701-. 



, . Bassani, A. G. Teix. J. 



Sc. 11 (1892) 93-. 

 , table, 12 place. Newman, F. W. [1876] 



Camb. Ph. S. T. 13 (1883) 145-. 



functions, tables. Glaisher, J. W. L. [1877] 

 Camb. Ph. S. T. 13 (1883) 243-. 



, theorejns. Glaisher, J. W. L. Mess. 



Mth. 5 (1876) 164-. 

 , theory. Graves, J. T. B. A. Ep. (1834) 



523-. 



, , arithmetical propositions derived 

 from. Lipschitz, . Liouv. J. Mth. 2 

 (1886) 219-. 



and imaginary quantities, theory. Wool- 

 house, W. S. B. Mth. Misc. 1 (1838) 336-. 



logarithmic quantities. Toblini, G. 

 Poligrafo 1 (1830) 21-. 



theorems, method. Strong, T. Silli- 



man J. 48 (1845) 36-. 

 other functions, treatment by equiangular 



spiral. Schellbach, C. H. Crelle J. 17 



(1837) 321-. 



Exponential series. Barfuss, F. W. Grunert 



Arch. 5 (1844) 155-. 

 , error in theorem. Fontana, G. Verona 



S. It. Mm. 2 (1784) 123-. 

 , inequalities. Tweedie, C. Edinb. Mth. 



S. P. 17 (1899) 33-. 



, connected with. Gibson, G. A. 

 Edinb. Mth. S. P. 18 (1900) 84-. 



and other expansions. Dupuis, N. F. 



Cn. E. S. P. & T. 7 (1890) (Sect. 3) 16-, 21-. 

 , sine, etc., series with alternating signs, 



sum. Unferdinger, F. Wien Sb. 56 (1867) 



(Ab. 2) 257-. 



symbolic operations. Scott, R. F. Mess. 

 Mth. 10 (1881) 142-. 



operators, theorems. Glaisher, J. W. L. 



QJ. Mth. 15 (1878) 266-. 



theorem. Schaeberle, J. M. A. Mth. 3 

 (1887) 156. 



transformation. Laisant, C. A. As. Fr. C. 

 E. (1879) 206-. 



and trigonometric functions, differentiation. 

 Martin, Art. Des Moines Anal. 6 (1879) 23-. 



Exponentials, expansion in a series of. Popoff, 

 A. [1874] Crelle J. Mth. 80 (1875) 204. 



, imaginary. Tarry, G. N. A. Mth. 14 

 (1895) 269-. 



, , expansion. Davies, T. S. Mathe- 

 matician 3 (1850) 66-. 



and logarithms, differentiation. Schlomilch, 

 0. Grunert Arch. 11 (1848) 386-. 



, expansion. Ocagne, M. d'. N. A. 



Mth. 1 (1882) 241-. 



as limiting values of ( 1 + - j , 



CUja - 1) n (n = oo ) . Wulf, T. Mh. Mth. Ps. 

 8 (1897) 43-. 



, theory, application of geometry. 

 Schulten, N. G. af. (vm) Helsingf . Acta 5 

 (1858) 437-. 



, successive, of Euler. Grillet, J. H. Liouv. 



J. Mth. 10 (1845) 233-. 

 , theory. Laurent, H. N. A. Mth. 13 



(1874) 5-. 

 Hyperbolic areas, and natural logarithms. 



Grunert, J. A. Grunert Arch. 25 (1855) 



82-. 



and cyclic sine and cosine, functions repre- 

 senting generalisation. Hellwig, C. Grunert 

 Arch. 35 (1860) 186-. 



functions. Fuss, N. [1810] St Pe"t. Ac. Sc. 

 Mm. 11 (1830) 220-. 



. Hottel, J. N. A. Mth. 3 (1864) 



416-. 

 . Azzarelli, M. Em. At. N. Line. 24 



(1871) 112-. 

 . Laisant, C. A. Bordeaux S. Sc. Mm. 



10 (1875) 233-. 

 . Gallatly, W. Mth. Gz. No. 5 (1895) 



40-. 

 . Haskell, M. W. N. Y. Am. Mth. S. 



Bll. 1 (1895) 155-. 



in connection with the hyperbola. 

 Crawford, L. Edinb. Mth. S. P. 13 (1895) 

 153-. 



, functions of. Nicodemi, R. G. Mt. 15 



(1877) 193-. 



306 



