This is a preview of subscription content, log in via an institution to check access.
References
In Mathesis, vol. 9 (1889), p. 75 and p. 110. In the latter note the case of the two functionsx 2 andx·✓x✓ is cited as an illustration. Further examples have been given by Bôcher in the articles hereafter cited. Peano has another paper on the same subject in the Rendiconti della R. Accademia dei Lincei, ser. 5, vol. 6, 10 sem. (1897), p. 413.
See also Bulletin of the American Mathematical Society, ser. 2, vol. 7 (1900), p. 120, and Annals of Mathematics, ser. 2, vol. 2 (1901), p 93. The properties of Wronskians of functions of a real variable have been further investigated by the same writer in the Bulletin of the American Mathematical Society, ser. 2, vol. 8 (1901), p. 53.
Cf. Bôcher, l. c., pp. 141, 142.
Cf. formula (4), p. 287.
Cf. E. Pascal, Die Determinanten (translation by Leitzmann), p. 39.
This theorem, as well as Theorem B in § 4, is taken directly from the paper already cited (Transactions of the American Mathematical Society, vol. 2 (1901), p. 139, Theorems IV and VI). Relations between other theorems of the same paper and those of the remaining sections of the present article are as follows: The exceptions made in Bôcher's Lemma II (p. 147) are removed in my Theorem VII, so that in his Theorem VIII the assumption that thenth derivatives of theu's are continuous is superfluous; some properties established in his discussion of Peano's theorems are generalized by my Theorem VIII; and Theorem XII of the present paper may be compared with his Theorem VII. Whenu (k)1 ,u (k)2 ,...,u (k)n are continuous, Theorem XI is equivalent to Theorem X of his article in the Bulletin of the American Mathematical Society (ser. 2, vol. 8 (1901), p. 59).
Cf. E. Pascal, Die Determinanten (translation by Leitzmann), pp. 193, 194.
See foot-note**), pp. 290 and 291.
Author information
Authors and Affiliations
Additional information
An announcement of some of the results of this paper, without proof, has appeared in the Bulletin of the American Mathematical Society, ser. 2, vol. 12 (1906), p. 482.
Rights and permissions
About this article
Cite this article
Curtiss, D.R. The vanishing of the wronskian and the problem of linear dependence. Math. Ann. 65, 282–298 (1908). https://doi.org/10.1007/BF01450000
Issue Date:
DOI: https://doi.org/10.1007/BF01450000