Colloquium publications.

DIVERGENT SERIES AND CONTINUED FRACTIONS. 171

25. Banning. Ueber Kugel- und Cylinderfunktionen und deren Kettenbruchentwickelung. Dissertation, Bonn, 1894, pp. 1-33.
26. Stieltjes. (a) Recherches sur les fractions continues. Annales de
Toulouse, vol. 8, J, pp. 1-122, and vol. 9, A, pp. 1-47. 1894-95.
Published also in vol. 32 of the Memoires presentes a l'Acad.
des sciences de l'Institut National de France.
A rich memoir, developing particularly the connection
between an important class of continued fractions and the corresponding integrals.
(a') Sur un d6veloppement en fraction continue. Comp.
Rend., vol. 99, p. 508, 1884.
(a") Same subject. Ibid., vol. 108 (1889), p. 1297.
(a"') Sur une application des fractions continues. Ibid., vol.
118 (1894), p. 1315.
(alv) Recherches sur les fractions continues. Ibid., vol. 118
(1894), p. 1401.
Markoff. (b) Note sur les fractions continues. Bull. de 1'Acad.
imp. des sciences de St. Petersbourg, ser. 5, vol. 2, pp. 9-13,
1895.
This gives a discussion of the relation of his work to that of
Stieltjes.
27. H. von Koch. (a) Sur un theoreme de Stieltjes et sur les fonctions
d6finies par des fractions continues. Bull. de la Soc. Math. de
France, vol. 23, pp. 33-40, 1895.
(a') Sur la convergence des determinants d'ordre infini et des
fractions continues. Comp. Rend., vol. 120, p. 144, 1895.
28. Markoff. Deux demonstrations de la convergence de certaines fractions continues. Acta Math., vol. 19, pp. 93-104, 1895.
Contained also in his Differenzenrechnung (deutsche Uebersetzung), chap. 7, ~ 21-22.
This discusses the convergence of the usual continued fraction for
f (y)dy
when f(y) > 0 between the limits of integration.
29. Pringsheim. Ueber die Convergenz unendlicher Kettenbriiche.
Sitzungsberichte der math.-phys. Classe der k. bayer'schen
Akad. der Wissenschaften, vol. 28, pp. 295-324, 1898.
The most comprehensive criteria for convergence yet obtained
are found in 29, 31, and 32b.