4030 



Logarithmic, Circular, Exponential Functions 



Gregory's series. Chartres, B. Nt. 42 (1890) 



341. 

 Hyperbolic base, analytical value. Hill, T. 



Am. As. P. 19 (1870) 21-. 



logarithms of first n-i numbers, formula 

 for. Tilly, J. M. de. Brux. Ac. Bll. 35 

 (1873) 30-. 



Logarithmic series, and series for tan" 1 6, with 

 alternating signs, sum. Unferdinger, F. 

 Wien Sb. 55 (1867) (Ab. 2) 75-, 332. 



Parabolic trigonometric functions. Egidi, G. 

 Em. N. Line. At. 47 (1894) 16-. 



trigonometry. Giinther, . D. Nf. Tbl. 

 (*1881) [20]-. 



Periodic functions, real, derived from equation 



i^V = F(x). Weierstrass, C. Berl. Mb. 



(1866) 97-, 185. 

 -- , simplest. Schellbach, C. H. Crelle J. 



48 (1854) 207-. 

 Periodicity of sin a; and cos a;. Studnicka, . 



Palermo Cir. Mt. Ed. 13 (1899) 378-. 

 Powers of sines, series, summation. Ritten- 



house, D. [1792] Am. Ph. S. T. 3 (1793) 



155-. 

 --- , , . Nulty, 0. [1816] Am. Ph. 



S. T. 1 (1818) 395-. 

 Problems. Adams, Jas. Thomson A. Ph. 13 



(1819) 188-. 

 Product series for cos x and summation for 



secx. Weyr, E. Bll. Sc. Mth. 12 (1888) 



25-. 

 Eepresentation of sine and cosine as infinite 



products. Hoppe, R. Grunert Arch. 27 



(1856) 170-. 

 Secant and tangent coefficients, formulae for 



determination. Schlomilch, 0. Grunert 



Arch. 16 (1851) 411-. 

 Series, value. Glaisher, J. W. L. [1878] Mess. 



Mth. 8 (1879) 127-. 

 Side of regular n gon, series for finding. 



Oppert, J. As. Fr. C. E. (1896) (Ft. 1) 



133. 



Sines of fourth order F 



Kapteyn, J. C., 



Kapteyn, W. Amst. Ak. Vh. 24 (1886) 98 pp. 

 Tangent and cotangent series, new deduction 



of Euler's. Studnicka, F. J. Prag Sb 



(1887) (Mth.-Nt.) 103-. 

 Transcendental functions, method of treatment 



differing from Euler's, and theorem. Pezzi, 



F. Verona S. It. Mm. 5 (1790) 417-. 

 Transformation involving de Moivre's theorem. 



Gamier, J. G. Brux. Ac. Bll. 6 (1839) 



151-. 

 ' Trigonometric and astronomical infinite series. 



Grunert, J. A. Grunert Arch. 18 (1852) 



420-. 

 ----- . Ligowski, W. Arch. Mth. Ps. 



56 (1874) 328-. 

 developments, and integration of trigono- 



metric functions. Richardson, J. M . Franklin 



I. J. 32 (1856) 409-. 



4030 



Trigonometric functions, integration of general 



classes. Philbrick, P. H. Des Moines Anal 



9 (1882) 177- ; 10 (1883) 9-. 

 , new researches. Lyetnikov, A. V. [1882] 



(XH) Eec. Mth. (Moscou) 10 (1882-83) 



(Ft. 1) 227-. 



, periodicity. Mantel, W. N. Arch. 

 Wisk. 3 (1898) 279-; Fschr. Mth. (1898) 

 376. 



, properties deduced from addition 

 theorems. Muirhead, R. F. Edinb. Mth. 

 S. P. 14 (1896) 127-. 



, two reciprocal relations, and application 



to 4 dimensions. Hoppe, R. Arch. Mth. 

 Ps. 67 (1882) 412- . 



and hyperbolic functions, multiplication. 

 Trzaska, W. Par. T. Nauk So. Pam. 10 

 (*1878) Art. 8, 7 pp. 



series. Dobinski, G. [1876] Arch. Mth. 

 Ps. 63 (1879) 380-. 



, Abel's transformation. Lerch, M- 

 Prag Ceske Ak. Fr. Jos. Ez. (Trida 2) 5 

 (1896) Art. 24, 5 pp. ; Fschr. Mth. (1896) 

 203. 



Trigonometry, Dr Stewart's theorems, analytical 



demonstration. Ellis, R. L. Camb. Mth. 



J. 2 (1841) 271-. 

 (Z + 2Z'cos0 + 2Z"cos</>')- n in series of cosines 



of multiples. Jacobi, C. G. J. Crelle J. 15 



(1836) 205-. 



. Bjorling, E. G. Stockh. 



Ofv. 6 (1849) 171- ; Grunert Arch. 21 (1852) 



26-. 

 . Dienger, J. Grunert Arch. 12 (1849) 



409-. 

 sin oo and cos oo . Glaisher, J. W. L. [1870] 



Mess. Mth. 5 (1871) 232-. 

 Usmx+ Fcos x + W. Hermite, C. Crelle J. 



76 (1873) 303-. 

 arc sin (x + iy) . Cayley, A. QJ. Mth. 15 (1878) 



. i? 1 -- 



J / (sin x, cos x) dx. Hermite, C. [1879?] 



G. Teiz. J. Sc. 2 (1880) 65-. 

 cos e + i sin 6, and its application to some 



equations. Airy, (Sir) G. B. [1887] Camb. 



Ph. S. P. 6 (1889) 104-. 

 So;*" 1 cos ka and similar series deduced from 



i* ^^a' Studnicka, F. J. Casopis 19 

 n 1 - xe ia 

 890) 113- ; Fschr. Mth. (1890) 261. 

 sm (xir) ^ continued pro d uc t for. McClintock, 



. N. Y. Mth. S. Bll. 2 (1893) 147-. 

 Sa: n arc tan K n ~ l = &7T/4, integral solutions. 



Stormer, C. C. E. 122 (1896) 175-, 225-. 

 sin 6, expression as an infinite product. Dixon, 



A. C. Mth. Gz. 1 (1900) 130-. 



LOGAEITHMIC AND EXPONENTIAL 

 FUNCTIONS. 



Compound interest, approximate calculation of 

 r. Lemannier, H. N. A. Mth. 3 (1864) 

 337-. l ' 



305 



