Hostname: page-component-66644f4456-2xp4c Total loading time: 0 Render date: 2025-02-13T07:53:12.140Z Has data issue: true hasContentIssue false
  • English
  • Français

XXIX.—On the Cardinal Function of Interpolation-Theory

Published online by Cambridge University Press:  15 September 2014

W. L. Ferrar
Get access

Extract

If we consider a set of values a0, an, a–n and a set of equidistant points x = a, a±nw, there are many interpolation formulæ which give functions assuming the values a0, an, a–n at the points x = a, a + nw, a − nw respectively. The function with which the present note deals is, writing π/w = m,

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 46 , 1927 , pp. 323 - 333
Copyright
Copyright © Royal Society of Edinburgh 1927

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 323 note * Proc. Roy. Soc. Edin., 35 (1915), 181–194CrossRefGoogle Scholar.

page 323 note † Acad. Belge: Classe des Sciences (1908), 319–410 ; in particular 336–352.

page 323 note ‡ Proc. Edin. Math. Soc., 34 (1915–1916), 3–10CrossRefGoogle Scholar.

page 323 note § Proc. Roy. Soc. Edin., 45 (1925), 269–282Google Scholar.

page 323 note ∥ Acta Math., 37 (1914), 75–112CrossRefGoogle Scholar.

page 323 note ¶ Math. Zeitschrift, 3 (1919), 93–113CrossRefGoogle Scholar.

page 323 note ** Proc. London Math. Soc., (2), 23 (1924), 149–171Google Scholar.

page 325 note * The expansion is really Cauchy's “F(x) is the sum of its polar elements,” cf. Œuvres, sér. ii, tome 7, p. 326.

page 328 note * Proc. London Math. Soc., (2), 1 (1903), 184Google Scholar.

page 330 note * Proc. London Math. Soc., (2), 7 (1909), 445–472Google Scholar.

page 331 note * Cf. Carslaw, , Fourier Series and Integrals (1921), p. 141, cor. iiGoogle Scholar.

page 332 note * Carslaw, , loc. cit., p. 160, iiiGoogle Scholar.

page 333 note * Ann. de l'Ecole Normale, 39 (1922)Google Scholar and 40 (1923).