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.
- Multivariate formal power series,
- multivariate Sheffer-type polynomials,
- multivariate Sheffer-type differential operators,
- multivariate weighted Stirling numbers,
- multivariate Riordan array pair,
- multivariate exponential polynomials.
Available at: http://works.bepress.com/tian_xiao_he/25/