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Note on an “Alternant” with Factorial Elements

Published online by Cambridge University Press:  20 January 2009

Zia-uddin
Zia-uddin
Affiliation:
University of Edinburgh.
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The alternant with powers of variables for its elements

has often been investigated and its properties are well known. In the present note an “alternant” with factorial elements,

will be discussed. Here a, b, c, …, z, α, β, γ, …, ω are integers such that

and

with the convention that a(0) = 1, O(0) = 1, and that, where negative indices occur (in the reductions of §2), the factorial is to be regarded as zero.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 4 , August 1933 , pp. 296 - 299
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

page 296 note 1 See, for example, Muir's History of Determinants.

page 298 note 1 The necessity for the convention a(0) = 1, O(0) = 1 is seen by examining the reduction of for the cases a≧1 and a=0.