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Notes on Fourier series (IV): Summability (R2)

Published online by Cambridge University Press:  24 October 2008

G. H. Hardy  and
W. W. Rogosinski
G. H. Hardy
Affiliation:
Trinity CollegeCambridge
W. W. Rogosinski
Affiliation:
King's CollegeNewcastle on Tyne
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Extract

1.1. There are two familiar methods of summation of divergent series usually called the methods (R, 1) and (R, 2). If sn = u0 + u1 + … + un and, as it will be convenient to suppose throughout, u0 = 0, then

when h → + 0§: the convergence of the series for small positive h is presupposed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 1 , January 1947 , pp. 10 - 25
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

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