4030 



Logarithmic, Circular, Exponential Functions 



3 or more variables. 



approximation. Didon, F. C. E. 70 (1870) 



749-. 

 functions analogous to sine and cosine. 



Glaisher, J. W. L. [1878] QJ. Mth. 16 



(1879) 15-. 

 integrability. Brunn, H. [1848J St Pe"t. Ac. 



Sc. Bll. 7 (1849) 126-. 

 integration. Minich, S. E. At. Sc. It. (1844) 



62-. 

 , formulae. Minich, S. E. Yen. Mm. I. 6 



(1856) 473-. 

 rational functions, representation, analytic. 



Mittag-Leffler, G. Stockh. Ofv. 34 (1877) 



A T o. 10, 3-, 17-. 

 theory. AW, M. [1875] Wien Ak. Sb. 72 



(1876) (Ab. 2) 289-. 

 . Capelli, A. Nap. Ed. 29 (1890) 297-. 



4030 Logarithmic, circular, 

 exponential functions. 



CIECULAE FUNCTIONS. 



Eaabe, J. L. Crelle J. 16 (1837) 219-. 

 Calculation of tables. Olivier, L. Crelle J. 2 



(1827) 252-. 



Circular arcs, reduction to imaginary logarithms. 

 Calandrelli, G. [1825] Mod. Mm. S. It. 20 



(1828) 45-. 



functions, analogues. Appell, P. C. E. 84 

 (1877) 1378-. 



, analysis. Eees, E. van. Quetelet Cor. 



Mth. 6 (1830) 277-. 



, analytic derivation. Tralles, J. G. 

 Berl. Ab. (1812-13) (Mth.) 161-. 



, theory. Chessin, A. S. Am. J. Mth. 



19 (1897) 217-. 

 , approximate formulas and application. 



Fein, A. (ix) Forster Al. Bauztg. 38 (1873) 



34-. 



, approximation by means of algebraic 

 functions. Laguerre, E. C. E. 90 (1880) 

 304-. 



, astronomical formulae. Le Verrier, 

 U. J. J. (x) Par. Obs. A. 1 (1855) 73-; 

 2 (1856) 301 + [167] pp.; 3 (1857) 199-, [1]-; 

 4 (1858) 1-, [1]-; 5 (1859) 1-; 6 (1861) 

 435 pp.; 10 (1874) 1-, [1]-; 11 (1876) 

 560 + [136] pp.; 12 (1876) 76 + [178] + A. 

 80 + [A. 286] pp. ; 13 (1876) 1-, [1]- ; 14 

 (1877) Ft. 1, A. 1-, [A. 1]-, Ft. 2, 1-, 

 [I]-- 



, differential, integration in finite form. 



Du Bourguet, . Gergonne 



(1813-14) 72-. 

 , , . Gruson, J. P. Berl. 



Ab. (1820-21) 44-. 



, differentiation, successive. Colombier, 

 P. A. G. N. A. Mth. 9 (1850) 29-; 1 (1862) 



, formula. Catalan, . As. Fr. C. E. 



(1889) (Pt. 1) 232. 



4030 



Circular functions, fundamental principles. 

 Sarrus, F. Gergonne A. Mth. 11 (1820-2li 

 323-. 



, properties, new proof. Fleck, 

 (I'abbe) J. M. (xn) Metz Ac. Mm. 54 

 (1874) 337-. 



, integration. Hermite, C. [1872] L. 



Mth. S. P. 4 (1871-73) 164-. 

 , inverse, differential coefficients. Wiiatley, 



F. Mth. Gz. 1 (1900) 83-. 



, 2nd order, integrals. Meyer, V. H. 

 Grunert Arch. 17 (1851) 426-. 



, principal values. Stolz, O. Innsb. Nt. 



Md. B. 17 (1887) 67-. 



, resolution into partial fractions. 

 Oliveira Eamos, J. C. d\ G. Teix. J. Sc. 7 

 (1886) 7-; Fschr. Mth. (1885) 231-. 



, de Stainville's theorem. Gergonne, J. D. 



Gergonne A. Mth. 13 (1822-23) 270-. 



, summation. Jarrett, T. B. A. Ep. 

 (1847) (pt. 2) 5. 



and hyperbolic functions. Imshenetskii, 

 V. G. (xn) Kazan Un. Mm. (1862) (Ps.- 

 Mth.) 19 pp. 



. Giudice, F. G. Mt. 27 (1889) 



124-. 

 , analogy. Mossotti, O. F. Tortolini 



A. 2 (1851) 474- ; Pisa A. Un. Tosc. 6 (1861) 



, logarithmic tables. Forti, A. 

 (vi Adds.) N. Cim. 17 (1863) 243-. 



, relations. Eealis, S. Mathesis 6 



(1886) 7-. 

 Concepts cos x and sin x, extension. Beyssell, 



. Grunert Arch. 31 (1858) 299-. 

 Cosines, sums of series of like powers. Eadicke, 



A. Mathesis 4 (1884) 161-. 

 Cotangent and cosecant, fractional series for, 



algebraic proof. Glaisher, J. W. L. [1880] 



QJ. Mth. 17 (1881) 211-. 

 Definite integrals containing circular functions. 



Haan, D. Bierens de. Haarl. Ntk. Vh. Mtsch. 



17 (1862) 199 pp. 



Expansion. 



Oliveira, C. B. Ev. Brazil. 3 (I860) 214-. 

 of arc in terms of tangent. Schlomilch, 0. 

 Grunert Arch. 16 (1851) 230-. 



circular and exponential functions. Ampere, 

 A. M. Gergonne A. Mth. 15 (1824-25) 

 369-. 



. Demoulin, A. Brux. Ac. Bll. 



19 (1890) 541-. 



cosines and sines of multiple arcs. Maiden, 

 H. Ph. Mg. 20 (1842) 113-. 



in powers of arc. Schellbach, C. H. 



Crelle J. 16 (1837) 363-. 



A. Mth. 4 terms of arc, and of arc in terms 



of tangent. Gergonne, J. D. Gergonne A. 

 Mth. 3 (1812-13) 344-. 



exponential in powers of sine and cosine of 

 arc. David, . [1882] Toul. Ac. Sc. Mm. 

 5 (1883) (San. I.) 148-. 



fractional powers of cosines. Crelle, A. L. 

 Gergonne A. Mth. 13 (1822-23) 213- ; Crelle 

 J. 7 (1831) 253-, 314-. 



303 



