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On Riemann summability of functions

Published online by Cambridge University Press:  24 October 2008

B. Kuttner
B. Kuttner
Affiliation:
University of Birmingham
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Extract

1. Let k be a positive integer. With the usual terminology, the series

will be said to be Riemann summable (R, k) to l if

converges for all sufficiently small x, and tends to l as x → 0. Here we take (sin nx)/(nx) as meaning 1 when n = 0. A more general summability method which has been considered by various authors ((1), (2), (5), (6), (8), (9), (10)), and is usually denoted by (ℜ, λ,k) is obtained by replacing (2) by

where λ = {λn} is a sequence of non-negative numbers increasing to ∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 83 - 94
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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