Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T00:19:02.742Z Has data issue: false hasContentIssue false
  • English
  • Français

XI.—On q-Functions and a certain Difference Operator

Published online by Cambridge University Press:  06 July 2012

F. H. Jackson
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper my object is, primarily, to investigate the properties of a certain operative symbol which appears to be of great utility in discussing q-functions. The first part of the paper will consist of an investigation into the various forms of

and the nature of the inverse operations symbolised by Δ−n. With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function of x.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 46 , Issue 2 , 1909 , pp. 253 - 281
Copyright
Copyright © Royal Society of Edinburgh 1909

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page 254 note * Trans. Roy. Soc. Edin., vol. xli. pp. 105–118, 399–407, etc. Proc. L.M.S., series 2, vol. ii. pp. 192–221; vol. iii. pp. 1–23.

page 254 note † Heine, , Kugelfunctionen, ed. 1878, pp. 99Google Scholaret seq; also Thomæ, Grelles Journal, vol. lxx.

page 255 note * Trans. Roy. Soc. Edin., vol. xii. pp. 1–28, 105–118, 399–408.

page 259 note * Cf. Boole, , Finite Differences, pp. 46Google Scholar, 47.

page 272 note * Proc. L.M.S., series 2, vol. ii. p. 196.

page 278 note * Proc. Roy. Soc., vol. lxxiv. p. 67.

page 278 note † Ibid., pp. 67–68.

page 280 note * Trans. R.S.E., vol. xli., pt. ii., p. 406.