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On the Evaluation of Certain Finite Sums of Progressive Products

Published online by Cambridge University Press:  04 July 2016

A. R. Collar
A. R. Collar*
Affiliation:
Sir George White Professor of Aeronautical Engineering, University of Bristol
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Extract

This note is concerned with the evaluation of the finite sum

where the m quantities Zi are arbitrary and where

is the binomial coefficient in a series of n terms. Summations of this kind appear in the evaluation of matrix products involving the reciprocal of order n of a segment of a Hilbert matrix or of a generalised Hilbert matrix. Such products are found, for example, in the representation of a lifting aerodynamical surface by a set of horseshoe vortices.

Let the m factors (r+Zi) be multiplied out, and let Pl be the sum ∑Zi, P2 the sum of the products taken in pairs, and so on; then

Type
Technical notes
Information
The Aeronautical Journal , Volume 63 , Issue 578 , February 1959 , pp. 118 - 119
Copyright
Copyright © Royal Aeronautical Society 1959

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References

1.Collar, A. R. (1950). On the Reciprocal of a Segment of a Generalised Hilbert Matrix. Proc. Camb. Phil. Soc, Vol. 47, Part I, 1950.Google Scholar
2.Collar, A. R. (1958). On the Accuracy of die Representation of a Lifting Line by a Finite Set of Horseshoe Vortices. The Aeronautical Quarterly, Vol. IX, p. 232, August 1958.Google Scholar