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Note on an Abstract Inversion Principle

Published online by Cambridge University Press:  20 January 2009

L. C. Hsu
L. C. Hsu
Affiliation:
Magdalene College, Cambridge.
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In a recent paper [1] of Bell, an abstract inversion principle has been formulated for inverting a type of finite series by employing operators. Bell's result involves Baker's general principle of cross-classification [2], Dedekind-Möbius inversion, L.C.M. inversion and some known generalisations. The purpose of this note is to introduce operators of negative degree and to formulate an inversion principle which covers more cases than Bell's.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 2 , November 1954 , pp. 71 - 73
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

[1]Bell, E. T., Duke Math. Journal, 15 (1948), 79–85.Google Scholar
[2]Baker, H. F., Proc. London Math. Soc., 21 (1891), 30–32.Google Scholar
[3]Hall, P., Quarterly Journal of Math. (Oxford), 7 (1936), 134–151.Google Scholar
[4]Weisner, L., Trans. American Math. Soc., 38 (1935), 485–492, 474–484.Google Scholar