Computation of generating functions for renewal sequences is performed by means of the multivariate Lagrange expansion formulae due to Good (1960), which yields the multifold analogue of Carlitz’ mixed generating function. As applications, the natural transition is demonstrated from Euler’s binomial theorem and the classical Vandermonde convolution formula to Abel identities and Hagen-Rothe formulas, as well as their multifold analogues due to Mohanty & Handa (1969) and Carlitz (1977), respectively.
Generating functions and combinatorial identities
CHU, Wenchang
1998-01-01
Abstract
Computation of generating functions for renewal sequences is performed by means of the multivariate Lagrange expansion formulae due to Good (1960), which yields the multifold analogue of Carlitz’ mixed generating function. As applications, the natural transition is demonstrated from Euler’s binomial theorem and the classical Vandermonde convolution formula to Abel identities and Hagen-Rothe formulas, as well as their multifold analogues due to Mohanty & Handa (1969) and Carlitz (1977), respectively.File in questo prodotto:
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