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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
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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
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(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