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On ‘translated quasi-Cesàro’ summability

Published online by Cambridge University Press:  24 October 2008

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

Corresponding to a fixed sequence {μn}, the Hausdorff method of summability (H, μn) is defined by the sequence-to-sequence transformation†

where we write

The quasi-Hausdorff method (H*, μn) is defined by the transformation

thus the matrix of the (H*, μn) transformation is the transpose of that of the (H*, μn) transformation. A method introduced by Ramanujan (9), which we will call‡ (S,μn) is given by the transformation

Thus the elements of row n of the matrix of the (S, μn) transformation are those of the corresponding row of the (H*, μn) transformation moved n places to the left.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 705 - 712
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

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