Generating functions and combinatorial identities

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\u27s 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