Interpolation and Combinatorial Functions | Zendy

VerdeStar Luis | Zendy

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Interpolation and Combinatorial Functions

Author(s) -

VerdeStar Luis

Publication year - 1988

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm198879165

Subject(s) - binomial coefficient , gaussian binomial coefficient , vandermonde matrix , mathematics , central binomial coefficient , stirling number , stirling numbers of the first kind , binomial (polynomial) , convolution (computer science) , interpolation (computer graphics) , polynomial , stirling numbers of the second kind , discrete mathematics , combinatorics , negative binomial distribution , mathematical analysis , statistics , computer science , animation , eigenvalues and eigenvectors , physics , computer graphics (images) , quantum mechanics , machine learning , artificial neural network , poisson distribution

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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