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Summability- (Z, p) and Sequences of Periodic Type

Published online by Cambridge University Press:  20 November 2018

J. D. Hill  and
W. T. Sledd
J. D. Hill
Affiliation:
Michigan State University
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We shall say that the sequence x = {sk} is summable- (Z, p) to the value s if

where p is a positive integer and

Ignoring the values of n, 1 — p ≤ n < 0, which are clearly irrelevant, the transformation (Z, p) coincides with the regular Nörlund transformation defined by the sequence ( 1 , 1 , . . . , 1, 0, 0 , . . .) containing p initial 1's. This class of methods was first studied systematically by Silverman and Szász (8).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 741 - 754
Copyright
Copyright © Canadian Mathematical Society 1964

References

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