Frobenius’ identity
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21: 16.23 Mathematical Applications
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►Many combinatorial identities, especially ones involving binomial and related coefficients, are special cases of hypergeometric identities.
In Petkovšek et al. (1996) tools are given for automated proofs of these identities.
22: 21.6 Products
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§21.6(i) Riemann Identity
… ►Then …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. …23: 25.10 Zeros
24: 27.8 Dirichlet Characters
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27.8.6
►A 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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25: 17.14 Constant Term Identities
26: 27.13 Functions
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27.13.5
►One of Jacobi’s identities implies that
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►Also, Milne (1996, 2002) announce new infinite families of explicit formulas extending Jacobi’s identities.
For more than 8 squares, Milne’s identities are not the same as those obtained earlier by Mordell and others.
27: 27.14 Unrestricted Partitions
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§27.14(v) Divisibility Properties
►Ramanujan (1921) gives identities that imply divisibility properties of the partition function. For example, the Ramanujan identity …implies . …For example, . …28: 26.3 Lattice Paths: Binomial Coefficients
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§26.3(iv) Identities
…29: 27.19 Methods of Computation: Factorization
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►Type II probabilistic algorithms for factoring rely on finding a pseudo-random pair of integers that satisfy .
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30: 20.7 Identities
§20.7 Identities
… ►Also, in further development along the lines of the notations of Neville (§20.1) and of Glaisher (§22.2), the identities (20.7.6)–(20.7.9) have been recast in a more symmetric manner with respect to suffices . … ►§20.7(v) Watson’s Identities
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20.7.15
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►This reference also gives the eleven additional identities for the permutations of the four theta functions.
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