4030 



Circular Functions, Expansion 



4030 



of fractions containing sines and cosines of 

 multiple arcs. Trembley, J. Berl. Mm. Ac. 

 (1802) 31-. 



in indefinite products. Gergonne, J. D. Ger- 

 gonne A. Mth. 1 (1810-11) 116-. 



of infinite products for trigonometric functions. 

 Schlomilch, 0. Schlomilch Z. 3 (1858) 

 389-. 



logarithmic, exponential and trigonometric 

 functions. Bangma, O. S. Amst. Mengel- 

 werk 2 (1816) 92-. 



powers of trigonometric ratios in series of 



of 6 a in powers of sin 6 . Scherk, H. F. Crelle 

 J. 11 (1834) 101-. 



(l + 2l'cos<p + 2l"cos<t>')- n in series of cosines 

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

 (1836) 205-. 



cos n (0 + A0) in powers of cos 0. Cauchy, 

 A. L. C. E. 15 (1842) 411-. 



sin-ia-. Raabe, J. L. Crelle J. 25 (1843) 

 169-. 



. Schlomilch, O. Schlomilch Z. 1 (1856) 



181-. 

 by Maclaurin's theorem. Chevilliet, . 



ascending powers of variable. Jeffery, H. M. N. A. Mth. 13 (1874) 209- 



[1860] QJ. Mth. 5 (1862) 91-. 



sines of multiple angles. Krafft, W. L. 

 [1802] St Pet. Ac. Sc. N. Acta 14 (1805) 

 290-. 



in products. Fade, H. N. A. Mth. 17 



(1898) 312-. 



trigonometric functions. Young, J. JR. Ph. 

 Mg. 5 (1834) 198-. 



as infinite products. Dienger, J, 

 Arch. Mth. Ps. 43 (1865) 474-. 



in infinite series. Burg, A. "Wien Jb. 



Pol. I. 19 (1837) 147-. 



products of binomial factors. 

 Rodriguez, O. Liouv. J. Mth. 8 (1843) 

 217-. 



in trigonometric series. Walton, W. [1871] 

 QJ. Mth. 12 (1873) 146-. 



of sinn0 and cosnfl. Eider, L. [1780] St 

 Pet. Ac. Sc. Mm. 5 (1815) 57-. 



in terms of sin 6 and cos 6, demonstra- 

 tion. Kausler, C. F. [1810] St Pet. Ac. 

 Sc. Mm. 4 (1813) 256-. 



(Euler). Fuss, N. [1813] St Pet. 



Ac. Sc. Mm. 6 (1818) 100-. 

 , cosn0 and sin" 6, cos" 0. Crelle, A. L. 

 Crelle J. 5 (1830) 197-. 



and cos nd in ascending powers of sin 

 and cos 0. Gregory, D. F. Camb. Mth. J. 

 2 (1841) 129-. 



terms of powers of sin 6 and 



cos0, by de Moivre's theorem. Sylvester, 



J. J. QJ. Mth. 4 (1861) 159-. 

 series of sines and cosines, of 



multiples of 0. Poisson, S. D. Par. EC. 



Pol. Cor. 2 (1809-13) 212- ; Ferussac Bll. 



Sc. Mth. 4 (1825) 140-, 344-. 

 . Kummer, E. E. Crelle J. 14 



(1835) 110-. 

 in terms of multiples of 0. Simony, 



0. Arch. Mth. Ps. 55 (1873) 64-. 



(a + bcosx) n , general term. Degen, C. F. 

 (vi Adds.) Kiob. Ov. (1819-20) 3-. 



cos" 6 in cosines of multiples of 0. Plana, G. 

 Gergonne A. Mth. 11 (1820-21) 84-. 



in sines and cosines of multiples of 6. 



Michel, P. Gergonne A. Mth. 13 (1822-23) 



cosines of multiples of d. Olivier, L. 



Crelle J. 1 (1826) 16-. 



tan d in powers of d, law. Bouvier, L. C. 

 Gergonne A. Mth. 14 (1823-24) 347-. 



(cosx), etc. Ohm, M. Ferassac Bll. Sc. 

 Mth. 5 (1826) 250-. 



0" in terms of sin 6. Scholtz, E. J. Crelle 

 J. 3 (1828) 70-. 



cos nx/cos n x and sin nxjcos" x in powers of 

 tan*. Arndt,F. Grunert Arch. 4 (1844)441-. 



sine and cosine in powers of arc. Schlomilch, 

 O. Grunert Arch. 5 (1844) 326-. 



cos n ax. Dienger, J. Grunert Arch. 11 

 (1848) 331-. 



cos m x in series of cosines for all values of n. 

 Neivman, F. W. Camb. and Dubl. Mth. J. 3 

 (1848) 61-. 



; in series of even multiples of <j>. 



l-/JiCOS<t> 



Wolfers, J. P. Grunert Arch. 21 (1853) 190-. 



sine and cosine. Grunert, J. A. Grunert 

 Arch. 29 (1857) 452-. 



sin rax and cosnx in powers of sin a; and 

 cos a;. Baehr, G. F. W. Amst. Vs. Ak. 10 

 (1860) 86-. 



. Yvon-Villarceau, 



A. J. F. C. R. 82 (1876) 1469-. 



. Catalan, E. C. N. A. Mth. 2 



(1883) 529-. 



sin a; and cos a;. Almqvist, P. W. Ts. Mt. 

 Fys. 3 (1870) 121-. 



in infinite series. Meusburger, K. 



Mh. Mth. Ps. 6 (1895) 256-. 

 in series of exponential functions with 



real exponents. Popov, A. T. (xn) Kazan 



Un. Mm. 11 (1875) 661-. 



cos n0 in powers of cosines, etc. Walton, 

 W. [1872] QJ. Mth. 12 (1873) 168-. 



sine and cosine of arc. Sang, E. [1877] 

 Edinb. E. S. P. 9 (1878) 400-. 



. David, . Par. S. Mth. 



Bll. 11 (1883) 72-. 



sec a; and tan a:. Andre, D. C. B. 88 

 (1879) 965-. 



cot x. Le Paige, C. M. M. H. H. C. E. 

 88 (1879) 1075-. 



(1 + b cos + &' cos ' + ...)". Oppolzer, T. 

 von. As. Nr. 105 (1883) 367-. 



- ~ . Catalan, E. C. Liege S. Sc. Mm. 



15 (1888) No. 1, 82-. 



sin n<j> and cos nip in powers of cos <j>. 

 Ocagne, M. d'. G. Teix. J. Sc. 9 (1889) 161-. 



tan -1 x, in convergent series. Saalschiltz, . 

 Konigsb. Schr. 40 (1899) [28]-. 



Function of 3 angles, first differentials of 



which are also to be regarded as angles. 



Schlafli, L. [1852] Crelle J. 48 (1854) 292-. 

 Functions of small angles, method of finding 



from five-figure tables. Pfeil, L. von. Arch. 



Mth. Ps. 58 (1876) 147-. 



304 



