hypergeometric identities

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1: 15.17 Mathematical Applications

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§15.17(iv) Combinatorics

►In combinatorics, hypergeometric identities classify single sums of products of binomial coefficients. …

2: 16.23 Mathematical Applications

… ►Many combinatorial identities, especially ones involving binomial and related coefficients, are special cases of hypergeometric identities. …

3: 16.4 Argument Unity

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§16.4(iii) Identities

… ►There are two types of three-term identities for ${}_3{}^{}F_2^{}$’s. … ► …

4: 15.4 Special Cases

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Chu–Vandermonde Identity

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5: 17.14 Constant Term Identities

§17.14 Constant Term Identities

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6: Bibliography B

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The hypergeometric identities of Cayley, Orr, and Bailey. Proc. London Math. Soc. (2) 50, pp. 56–74.

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External Links:

Document, MathReview (N. A. Hall), ZentralBlatt

Referenced by:

§15.16.

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7: 17.8 Special Cases of ${}_r{}^{}\psi _r^{}$ Functions

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Quintuple Product Identity

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8: 16.2 Definition and Analytic Properties

… ►Note that if $-m$ is the value of the numerically largest $a_j$ that is a nonpositive integer, then the identity …

9: 17.9 Further Transformations of ${}_{r+1}{}^{}\varphi _r^{}$ Functions

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$q$-Sheppard Identity

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10: 17.12 Bailey Pairs

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