Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T01:02:28.724Z Has data issue: false hasContentIssue false
  • English
  • Français

Nörlund Methods of Summability Associated with Polynomials

Published online by Cambridge University Press:  20 January 2009

D. Borwein
D. Borwein
Affiliation:
St Salvator's College, University of St Andrews
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let s, sn(n = 0, 1, …) be arbitrary complex numbers, and let

be a polynomial, with complex coefficients, which satisfies the normalizing condition

Associated with such a polynomial is a Nörlund method of summability Np: the sequence {sn} is said to be Np-convergent to s, and we write sn →s (Np), if

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , Issue 1 , June 1960 , pp. 7 - 15
Copyright
Copyright © Edinburgh Mathematical Society 1960

References

REFERENCES

(1)Borwein, D. and Boyd, A. V., Binary and ternary transformations of sequences, Proc. Edin. Math. Soc, 11 (1959), 175–181.Google Scholar
(2)Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
(3)Kubota, T., Ein Satz über den Grenzwert, Tôhoku Math. Journal, 12 (1917), 222–224.Google Scholar
(4)Silverman, L. L. and Szasz, O., On a class of Nörlund matrices, Annals of Math., 45 (1944), 347–357.Google Scholar