Chu–Vandermonde identity
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21: 1.1 Special Notation
22: 4.8 Identities
23: 20.11 Generalizations and Analogs
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βΊThis is the discrete analog of the Poisson identity (§1.8(iv)).
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βΊIn the case
identities for theta functions become identities in the complex variable , with , that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7).
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βΊSimilar identities can be constructed for , , and .
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24: 21.7 Riemann Surfaces
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βΊ
§21.7(ii) Fay’s Trisecant Identity
… βΊwhere again all integration paths are identical for all components. Generalizations of this identity are given in Fay (1973, Chapter 2). … βΊ§21.7(iii) Frobenius’ Identity
…25: 16.23 Mathematical Applications
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βΊMany combinatorial identities, especially ones involving binomial and related coefficients, are special cases of hypergeometric identities.
In PetkovΕ‘ek et al. (1996) tools are given for automated proofs of these identities.
26: 21.6 Products
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βΊ
§21.6(i) Riemann Identity
… βΊThen …This is the Riemann identity. On using theta functions with characteristics, it becomes …Many identities involving products of theta functions can be established using these formulas. …27: 25.10 Zeros
28: 27.8 Dirichlet Characters
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βΊ
27.8.6
βΊA Dirichlet character is called primitive (mod ) if for every proper divisor of (that is, a divisor ), there exists an integer , with and .
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27.8.7
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