Interpolation and Combinatorial Functions
Luis Verde‐Star
Source abstract
Using some basic results about polynomial interpolation, divided differences, and Newton polynomial sequences we develop a theory of generalized binomial coefficients that permits the unified study of the usual binomial coefficients, the Stirling numbers of the second kind, the q ‐Gaussian coefficients, and other combinatorial functions. We obtain a large number of combinatorial identities as special cases of general formulas. For example, Leibniz's rule for divided differences becomes a Chu‐Vandermonde convolution formula for each particular family of generalized binomial coefficients.
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