Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T13:06:03.104Z Has data issue: false hasContentIssue false
  • English
  • Français

On Perron's method of summation

Published online by Cambridge University Press:  24 October 2008

B. Kwee
B. Kwee
Affiliation:
University of Malaya, Kuala Lumpur, Malaya
Get access Rights & Permissions [Opens in a new window]

Extract

Let λ > 0 and let

If , we say that the series is summable (P, λ) to s.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1033 - 1040
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Perron, O.Beitrag zur Theorie divergenten reihen. Math. Z. 6 (1920), 286–310.CrossRefGoogle Scholar
(2)Szasz, O.On a summation method of O. Perron. Math. Z. 52 (1949–1950), 631–636.CrossRefGoogle Scholar
(3)Hardy, G. H.Divergent series (Oxford University Press).Google Scholar
(4)Agnew, R. P.Abel transforms and partial sums of Tauberian series. Ann. of Math. 50 (1949), 110–117.CrossRefGoogle Scholar
(5)Ramanujan, M. S.On Hausdorff and quasi-Hausdorff methods of summability. Quart. J. Math. (Oxford), (2), 8 (1957), 197–213.CrossRefGoogle Scholar
(6)Ishiguro, K.On the summability methods of divergent series. Acad. Roy. Belg. Cl. Sci. Mém. Coll. in −8°, 35 (1965), 1–43.Google Scholar
(7)Kuttner, B.On ‘translated quasi-Cesàro’ summability. Proc. Cambridge Philos. Soc. 62 (1966), 705–712.CrossRefGoogle Scholar
(8)Borwein, D.Theorems on some methods of summability. Quart. J. Math. (Oxford), (2), 36 (1958), 310–316.CrossRefGoogle Scholar