Colloquium publications.

174

THE BOSTON COLLOQUIUM.

Jour. fur Math., vol. 32, pp. 210-212, 1846.
(b) Untersuchung fiber die (selbe) Reihe. Ibid., vol. 34, pp. 285 -328, 1847.
(c) Ueber die Zahler und Nenner der Niherungswerthe von Kettenbriiche. Ibid., vol. 57, pp. 231-247, 1860.
Christoffel (d) Zur Abhandlung "Ueber Zahler und Nenner"
(u. s. w.) des vorigen Bandes. Ibid., vol. 58, pp. 90-91, 1861.
41. Thomae. Beitrige zur Theorie der durch die Heine'sche Reihe
darstellbaren Funktionen. Jour. fur Math., vol. 70, 1869. See
pp. 278-281 where the convergence of Heine's continued fraction is proved.
See also 32a.
42. (On Eisenstein's continued fractions).
Heine. (a) Verwandlung von Reihen in Kettenbriiche. Jour. fur
Math., vol. 32, pp. 205-209, 1846.
See also vol. 34, p. 296.
Muir. (b) On Eisenstein's continued fractions. Trans. Roy. Soc.
of Edinburgh, vol. 28, part 1, pp. 135-143, 1877.
Muir plainly was not aware of the preceding memoir by
Heine.
E. The Continued Fraction of Stieltjes. (See No. 26.)
43. Borel. Les series de Stieltjes, Chap. 5 of his Memoire sur les
series divergentes. Ann. del' Ec. Nor., ser. 3, vol. 16, pp. 107 -128; and also chap. 2 of his treatise, Les Series divergentes,
pp. 55-86, 1901.
44. Pade. Sur la fraction continue de Stieltjes. Comp. Rend., vol. 132,
p. 911, 1901.
45. Van Vleck. On an extension of the 1894 memoir of Stieltjes.
Trans. Amer. Math. Soc., vol. 4, pp. 297-332, 1903.
See also Nos. 27, 102.
F. The Continued Fraction for
1 + mx + m(a +- n)x2 + m(m + n) (m + 2n)x' +...
and its special cases.
46. Euler. (a) De seriebus divergentibus. Novi commentarii Acad.
scientiarum imperialis Petropolitanse, vol. 5, pp. 205-237, 1754 -5; in particular pp. 225 and 232-237.
(b) De transformatione seriei divergentis
1 - mx + m(m -+ n)x2 - m(m + n) (m + 2n)x3 + *. -