Original scientific paper

Generating functions and combinatorial identities

Chu Wenchang

Abstract

Computation of generating functions for renewal sequences is performed by means of the multivariate Lagrange expansion formulae dus 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.

Keywords

Binomial coefficients; multinomial coefficients; Vandermonde convolutions; generating functions; Lagrange inversion formulae

Hrčak ID:

8166

URI

https://hrcak.srce.hr/8166

Publication date:

1.6.1998.

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