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A convolution involving Bell polynomials

Published online by Cambridge University Press:  24 October 2008

G. P. M. Heselden
G. P. M. Heselden
Affiliation:
Admiralty Research Laboratory, Teddington, Middlesex
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Abstract

A convolution formula is established for Bell polynomials. This is expressed in seven equivalent ways and used to derive further properties of these polynomials. The application of these results to some twenty-seven special polynomial sets is shown and illustrated in the case of binomial, Hermite, Gegenbauer and generalized Bernoulli sets.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 97 - 106
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Bell, E. T.Exponential polynomials. Ann. of Math. 35 (1934).CrossRefGoogle Scholar
(2) The Bateman Project. Authors Erdelyi, A. et al. Higher transcendental functions (McGraw-Hill, 1955).Google Scholar
(3)Riordan, J.An introduction to combinatorial analysis. John Wiley and Sons, 1958.Google Scholar
(4)Kendall, M. G.The advanced theory of statistics (Charles Griffin and Co., London, 1945).Google Scholar
(5)Kendall, M. G. and Stuart, A.The advanced theory of statistics (C. Griffin and Co. London, 1966).Google Scholar
(6)Littlewood, D. E.The theory of group characters and matrix representations of groups (Clarendon Press Oxford, 1950).Google Scholar
(7)Rainville, E. D.Special Functions (Macmillan, New York, 1960).Google Scholar