Colloquium publications.

DIVERGENT SERIES AND CONTINUED FRACTIONS. 185

VIII. Approximation to a Function at More Than One Point. Connection
of Continued Fractions with the Theory of Interpolation.
Untder No. 99 have been already classified various works
which relate to simultaneous approximation at several points.
In addition, the following memoirs may also be consulted:
110. Cauchy. Sur la formule de Lagrange relativ a interpolation.
Analyse Alg., p. 528, or Oeuvres, ser. 2, vol. 3, pp. 429-433,
111. Jacobi. Ueber die Darstellung eine Reihe gegebner Werthe durch
eine gebrochene rationale Function. Jour. ffir Math., vol. 30,
pp. 127-156, 1846, or Werke, vol. 3, p. 479.
112. Pade. Sur l'extension des proprietes des reduites d'une fonction
aux fractions d'interpolation de Cauchy. Comp. Rend., vol.
130, p. 697, 1900.
See also Nos. 95, 99.
For general works upon interpolation which bring out the
relation of the subject to continued fractions, see Heine's
Handbuch der Kugelfunctionen, vol. 2, and Markoffs Differenzenrechnung (deutsche Uebersetzung), chap. 1, 6, 7; also the
following memoir:
113. Posse. Sur quelques applications des fractions continues algebriques. Pp. 1-175, 1886.
114. Gauss. Methodus nova integralium valores per approximationem
inveniendi. Werke, vol. 3, pp. 165-196, 1816.
115. Christoffel. Ueber die Gaussische Quadratur und eine Verallgemeinerung derselben. Jour. fir Math., vol. 55, pp. 61-82, 1858.
116. Mehler. Bemerkungen zur Theorie der mechanischen Quadraturen.
Ibid., vol. 63, pp. 152-157, 1864.
117. Posse. Sur les quadratures. Nouvelles Ann. de Math., ser. 2,
vol. 14, pp. 49-62, 1875.
118. Stieltjes. (a) Quelques recherches sur la theorie des quadratures
dites mecaniques. Ann. de l'Ec. Nor., ser. 3, vol. 1, pp. 409 -426, 1884.
We find here the origin of his notable 1894 memoir, No. 26a.
(a') Sur l'evaluation approchee des integrales. Comp. Rend.,
vol. 97, pp. 740 und 798, 1883.
(b) Note sur 1' integrale f(x)G(x)dx.
Nouv. Ann. de Math., ser. 3, vol. 7, pp. 161-171, 1888.
119. Markoff. Sur la methode de Gauss pour le calcul approche des integrales. Math. Ann., vol. 25, pp. 427-432, 1885.