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Concavity properties for certain linear combinations of Stirling numbers

Published online by Cambridge University Press:  09 April 2009

J. C. Ahuja
J. C. Ahuja
Affiliation:
Portland State University Portland, Oregon, U. S. A.
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In the notation of Riordan ([5], p. 33), the Stirling numbers, s(n, k) and S(n, k), of the first and second kind respectively are defined by the relation where (x)n = x(x − 1) … (x − n + 1) is the factorial power function. They have been used by Jordan ([3], p. 184) to define the numbers C(m, k) and D(m, k), as linear combinations of s(n, k) and S(n, k) respectively, given by where and and where and D(m, O.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 145 - 147
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities (University Press, Cambridge, 1952).Google Scholar
[2]Harper, L. H., ‘Stirling behavior is asymptotically normal’, Ann. Math. Statist. 38 (1967), 410–414.CrossRefGoogle Scholar
[3]Jordan, C., Calculus of Finite Differences (Chelsea, New York, 1950).Google Scholar
[4]Lieb, E. H., ‘Concavity properties and a generating function for Stirling numbers’. J. Combinatorial Theory 5 (1968), 203–206.CrossRefGoogle Scholar
[5]Riordan, J., An Introduction to Combinatorial Analysis (Wiley, New York, 1958).Google Scholar