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Multiple Series Manipulations and Generating Functions

Published online by Cambridge University Press:  20 November 2018

R. C. Grimson*
Affiliation:
Department of Biostatistics, School of Public Health, University of North Carolina, Chapel HillNorth Carolina27514
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Let γ be an increasing function on the real numbers such that γ(0) = 0 (which, by translation of axes, is no restriction) and suppose that γ(n) is a positive integer if n is a positive integer. Let γ- denote the inverse function of γ. Furthermore, let L(x) be the least integer ≥ x; let [x] be the greatest integer ≤x, and suppose that c0, c1 … is an arbitrary sequence of numbers.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Carlitz, L., q-Bernoulli and Eulerian number, Trans. Amer. Math. Soc. 76 (1954), 333-350.Google Scholar
2. Gould, H. W., Generalization of a bracket function of L. Moser, Canadian Math. Bull. 6 (1963), 275-277; Editor's Comment. 277-278.Google Scholar
3. Grimson, R. C., Some partition generating functions, Proceedings of the Fourth Southeastern Conference on Combinatorics, Graph Theory and Computing, 1973, 299-308.Google Scholar
4. Grimson, R. C., A summation formula and some properties of Eulerian functions, Proc. Amer. Math. Soc. 53 (1975), 290-292.Google Scholar
5. Roselle, D. P., Generalized Eulerian functions and a problem in partitions, Duke Math. J. 33 (1966), 293-304.Google Scholar
6. Über, Zeller Summen von grössten Janzen bei arithmetischen Reihen, Gött Nachr. 197, 243-268.Google Scholar