Abstract
With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.
| Original language | American English |
|---|---|
| Journal | Bulletin of the Institute of Mathematics, Academia Sinica |
| Volume | 1 |
| State | Published - 2006 |
Keywords
- Multivariate formal power series
- multivariate Riordan array pair
- multivariate Sheffer-type differential operators
- multivariate Sheffer-type polynomials
- multivariate exponential polynomials.
- multivariate weighted Stirling numbers
Disciplines
- Applied Mathematics
- Mathematics