Multivariate Expansion Associated with Sheffer-type Polynomials and Operators
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چکیده
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(t̂)f(ĝ(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. AMS Subject Classification: 05A15, 11B73, 11B83, 13F25, 41A58
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تاریخ انتشار 2006