Colloquium publications.

176

THE BOSTON COLLOQUIUM.

ubi simul egregise observationes circa fractiones continuas occurrent. Acta Acad. scientiarum imperialis Petropolitanae, 1784,
pars posterior, pp. 62-84, 1782.
(b) Summatio fractionis continuse cujus indices progressionem
arithmeticam constituunt. Opuscula Analytica, vol. 2, pp. 217 -239, 1785.
55. Spitzer. (a) Darstellung des unendlichen Kettenbruchs
1 1 1
x + 1 -- x + 2 + x + 3 +
in geschlossener Form, nebst anderen Bemerkungen. Archiv
der Math. und Phys., vol. 30, pp. 81-82, 1858.
(b) Darstellung des unendlichen Kettenbruchs
2x+1+ 1 1 1
1 2x + 3 + 2x + 5 + 2x + 7 +
in geschlossener Form. Ibid., vol. 30, pp. 331-334, 1858.
(c) Note fiber eine Kettenbriiche. Ibid., vol. 33, pp. 418-420,
1859.
(d) Darstellung des unendlichen Kettenbruches
m m
)<x) 2n(2x + 1) ++-!(x) = n(2x + 1) +- n(2x + 3) - n(2x + 5) +
in geschlossener Form. Ibid., vol. 33, pp. 474-475, 1859.
56. Laurent. (a) Note sur les fractions continues. Nouvelles Ann. de
Math., ser. 2, vol. 5, pp. 540-552, 1866.
This treats the continued fraction
x x x
1 eyer. () Uebe eine Eigenschaft des Kettenbuches +
E. Meyer. (b) Ueber eine Eigenschaft des Kettenbruches
1
x - - - Archiv der Math. und Phys., ser. 3, vol. 5,
x - x -
p. 287, 1903.
Meyer's results will be found on p. 548 of Laurent's memoir
and differs only in that x has been replaced by - 1/x2.
57. Schlomilch. (a) Ueber den Kettenbruch fur tan z. Zeitschrift fir
Math. und Phys., vol. 16, pp. 259-260, 1871.
Glaisher. (b) A continued fraction for tan nx. Messenger of
Math., ser. 2, vol. 3, p. 137, 1874.
(c) Note on continued fractions for tan nx. Ibid., ser. 2, vol. 4,
pp. 65-58, 1875.