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A generalization of the Sα-summation method

Published online by Cambridge University Press:  24 October 2008

A. Meir  and
A. Sharma
A. Meir
Affiliation:
University of Alberta
A. Sharma
Affiliation:
University of Alberta
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Extract

In 1949, Meyer-König (5) introduced the so-called Sα-method of summability which is one of a family of transformations including the Euler, Borel and Taylor methods. Later in 1959, Jakimowski (3) defined the [F, dn] transformation which includes the Euler method as a special case. If {dn} is given infinite sequence and E denotes the displacement operator (i.e. Eks0 = sk), then the [F, dn] transformation of {sn} is given by {tn} where

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 61 - 66
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Agnew, R. P.Euler transformations. Amer. J. Math. 66 (1944), 313–337.Google Scholar
(2)Ishiguro, K.Über das S α-Verfahren bei Fourier–Reihen. Math. Z. 80 (1962) 44–11.CrossRefGoogle Scholar
(3)Jakimovski, A.A generalization of the Lototsky method of summability. Michigan Math. J. 6 (1959), 277–290.CrossRefGoogle Scholar
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(5)Meybb-König, W.Untersuchungen über einige verwandte Limitierungsverfahren. Math. Z.. 52 (1950), 257–304.CrossRefGoogle Scholar