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Note on a special determinant

Published online by Cambridge University Press:  31 October 2008

A. C. Aitken
A. C. Aitken
Affiliation:
University of Edinburgh.
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Suppose a polynomial or convergent power series

is raised to powers j = 0, 1, 2, 3, … The coefficients of xk in [f(x)]j, k = 0, 1, 2, …, may be entered as elements in positions (j, k) in an array or matrix F, thus:

By construction all elements in column (k) have weight (sum of suffixes) equal to k.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 30 , January 1937 , pp. xxvii - xviii
Copyright
Copyright © Edinburgh Mathematical Society 1937