Article
Symbolization of generating functions; an application of the Mullin–Rota theory of binomial enumeration
Computers and Mathematics with Applications
(2007)
Abstract
We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.
Keywords
- Generating function,
- symbolic sum formula,
- binomial enumeration,
- shift-invariant operator,
- delta operator,
- Bell number,
- Genocchi number,
- Euler number,
- Euler polynomial,
- Eulerian fraction,
- Bernoulli number,
- Bernoulli polynomial
Disciplines
Publication Date
2007
Publisher Statement
Computers & Mathematics with Applications is published by Elsevier, http://www.journals.elsevier.com/computers-and-mathematics-with-applications/.
Citation Information
Tian-Xiao He, Peter J.S. s and Leetsch C. Hsu. "Symbolization of generating functions; an application of the Mullin–Rota theory of binomial enumeration" Computers and Mathematics with Applications Vol. 54 (2007) Available at: http://works.bepress.com/tian_xiao_he/23/