2815 Continued fractions 



convergents. Bartholomew, F. Grunert Arch. 



18 (1852) 328-. 



. Heine, H. E. Crelle J. 57 (I860) 231-. 

 . Christoffel, E. B. Crelle J. 58 (1860) 



90-. 



. Muir, T. B. A. Kp. (1876) (Sect.) 27-. 

 . Vahlen, K. T. Crelle J. Mth. 115 (1895) 



221-. 

 , abnormal, of a function, distribution. Fade, 



H. C. E. 130 (1900) 102-. 

 , differences. Dormoy, H. N. A. Mth. 5 



(1846) 132-. 

 , errors of principal and subsidiary. Har- 



greaves, R. Mess. Mth. 27 (1898) 152-. 

 , generalisation. Barbier, E. C. E. 98 



(1884) 1531-. 

 , law of formation, blinding, E. F. A. 



St Pet. Ac. Sc. Bll. 13 (1869) 524-. 

 , , Euler's. Schlegel, 8. F. V. Z. 



Mth. Ps. 22 (1877) 402-. 

 , resultants. Gegenbauer, L. Amst. Ak. Vs. 



5 (1897) 289-. 

 and convergents, relation. Seidel, L. Munch. 



Ab. 7 (1855) 559-. 

 converging, application of determinants. 



Ramus, G. Kiob. Ov. (1856) 106-. 



fractions and converging multiples. Hea- 

 wood, P. J. Mess. Mth. 26 (1897) 79-. 



for cube roots. Seeling, P. Grunert Arch. 8 



(1846) 69-. 

 . Cordon*, G. G. Mt. 32 (1894) 183-. 



definite integral I F (x) dx. Stieltjes, . 



C. E. 99 (1884) 508^! 



integrals. Stieltjes, . C. E. 108 (1889) 



1297-. 



descending power series. Stieltjes, T. J. 

 Toul. Fac. Sc. A. 3 (1889) H, 17 pp. 



. Cebysev, P. [1892] St Pet. Ac. 



Sc. Mm. (Rs.) 71 (1893) (Suppl.) No. 3, 73 pp. ; 



Fschr. Mth. (1892) 192-. 

 development. Schendel, L. Crelle J. Mth. 80 



(1875) 95-. 

 , geometrical view. Klein, F. Gott. Nr. 



(1895) 357-. 

 doubly periodic. Kahl, E. Grunert Arch. 19 



(1852) 158-. 

 for e. Hurwitz, . Konigsb. Schr. 32 (1891) 



(So.) 59-. 

 and e e . Sundman, K. F. Helsingf. Ofv. 



38 (1896) 57-. 



e F( *>. Laguerre, E. Liouv. J. Mth. 6 

 (1880) 99-. 



gtan- 1 !;). Laguerre, E. Par. S. Mth. Bll. 5 



(1877) 95-. 

 Eisenstein's. Muir, T. [1877] Edinb. E. S. 



T. 28 (1879) 135-. 

 equal. Heilermann, . Schlomilch Z. 5 



(1860) 362-. 

 Euler's ; and Wallis's theorem. Bauer, G. 



[1872] Munch. Ab. 11 (1873) (Ab. 2) 97-. 

 expansion in series by means of. Chebuishev, 



P. L. [1865] (xn) Eec. Mth. (Moscou) [1] 



(1866) 291-. 

 forms of numbers determined by. Roberts, S. 



[1878] L. Mth. S. P. 10 (1878-79) 29-. 



Continued fractions 2815 



for fraction 1 .3 .5 ... (2-l)/2 .4 .6 ... 2n. 

 Stieltjes, . QJ. Mth. 25 (1891) 198-. 



function (l + x) n . Fade, H. C. E. 129 

 (1899) 753-, 875-. 



Gauss's theorems, proof. Clausen, T. Crelle 



J. 3 (1828) 311. 

 generalisation. Lejeune-Dirichlet, G. Berl. B. 



(1842) 93-. 

 . Jacobi, C. G. J. Crelle J. 69 (1868) 29-. 



(Jacobi). Bachmann, P. [1872] Crelle J. 

 75 (1873) 25-. 



. Poincare,H. C. E. 99 (1884) 1014-. 



. Minkowski, H. Par. EC. Norm. A. 13 



(1896) 41-. 

 geometric application. Leger, E. Quetelet 



Cor. Mth. 9 (1837) 483-. 



interpretation. Lieblein, J. Z. Mth. Ps. 12 

 (1867) 185-. 



indefinite, transformation to vulgar fractions. 



Pezzi, F. Mod. S. It. Mm. 11 (1804) 410-. 

 infinite. Schulten, N. G. af (fil.) [1844-47] 



Helsingf. Acta 2 (1847) 661- ; 3 (1852) 427-. 

 . Spitzer, S. Grunert Arch. 33 (1859) 418-. 

 . Studnicka, F. J. Prag Sb. (1892) (Mth. 



Nt.) 254- ; Casopis 22 (1893) 15-. 

 Convergence. Pringsheim, A. Munch. Ak. 



Sb. 28 (1899) 295- ; 30 (1901) 233. 

 , evaluation. Spitzer, S. Grunert Arch. 30 



(1858) 331- ; 33 (1859) 474-. 

 for infinite series. Buzengeiger, K. H. J. Zach 



M. Cor. 22 (1810) 513-. 

 . Muir,T. Edinb. E. S. T. 27 (1876) 



467-. 



irrational numbers. Gylden, H. C. E. 106 

 (1888) 1584-, 1777-. 



("e-^dx. Jacobi, G. G. J. Crelle J. 12 



(1834) 346-. 

 Jacobi 's formula 



^~ = C sin [ (n + 1) cos" 1 x\. 



Hermite, C. [1875] Liege S. Sc. Mm. 6 (1877) 



No. 7, 7 pp. 

 law of formation. Giinther, S. [1875] Wien 



Ak. D. 36 (1876) (,16. 2) 187-. 

 for nth roots. Seeling, P. Arch. Mth. Ps. 46 



(1866) 80-. 

 for nth surds. Hoffmann, K. E. Arch. Mth. 



Ps. 64 (1879) 9-. 

 with negative quotients. Saalschiitz, L. Crelle 



J. Mth. 120 (1899) 132-, 242-, 354. 

 negative, for square roots. Stern, M. A. [1864] 



Gott. Ab. 12 (1866) 48 pp. 

 numerical values. Glaisher, J. W. L. [1874] 



QJ. Mth. 13 (1875) 255-. 

 periodic. Kramp, C. Gergonne A. Mth. 1 



(1810-11) 261-, 319-. 

 . Galois, E. Gergonne A. Mth. 19 (1828- 



29) 294-. 

 . Lebesgue, V. A. Ferussac Bll. Sc. Mth. 



15 (1831) 155-. 

 . Ramus, C. Kiob. Ov. (1836-37) 1-; 



Kjtfb. Dn. Vd. Selsk. Afh. 7 (1838) 197- ; 



Crelle J. 20 (1840) 13-. 

 . Broager, P. D. Kjtfb. Dn. Vd. Selsk. 



Afh. 8 (1841) 145-. 



199 



