Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T08:21:26.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiple Series Manipulations and Generating Functions

Published online by Cambridge University Press:  20 November 2018

R. C. Grimson
R. C. Grimson*
Affiliation:
Department of Biostatistics, School of Public Health, University of North Carolina, Chapel HillNorth Carolina27514
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 103 - 106
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