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XXIX.—On the Cardinal Function of Interpolation-Theory

Published online by Cambridge University Press:  15 September 2014

W. L. Ferrar
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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,

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

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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.

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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.

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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).