Fay trisecant identity

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11: 15.17 Mathematical Applications

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§15.17(iv) Combinatorics

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

12: 27.15 Chinese Remainder Theorem

… ►The Chinese remainder theorem states that a system of congruences $x\equiv a_1(mod{m}_1),\mathrm{\dots },x\equiv a_k(mod{m}_k)$, always has a solution if the moduli are relatively prime in pairs; the solution is unique (mod $m$), where $m$ is the product of the moduli. …

13: 17.17 Physical Applications

… ►In exactly solved models in statistical mechanics (Baxter (1981, 1982)) the methods and identities of §17.12 play a substantial role. …

14: 17.18 Methods of Computation

… ►Lehner (1941) uses Method (2) in connection with the Rogers–Ramanujan identities. …

15: 35.10 Methods of Computation

… ►Koev and Edelman (2006) utilizes combinatorial identities for the zonal polynomials to develop computational algorithms for approximating the series expansion (35.8.1). …

16: David M. Bressoud

… ►His books are Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No. …

17: 1.1 Special Notation

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$x,y$	real variables.
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$𝐈$	identity matrix
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18: 4.8 Identities

§4.8 Identities

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§4.8(i) Logarithms

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§4.8(ii) Powers

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19: 20.11 Generalizations and Analogs

… ►This is the discrete analog of the Poisson identity (§1.8(iv)). … ►In the case $z=0$ identities for theta functions become identities in the complex variable $q$, 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). … ►Similar identities can be constructed for ${}_2{}^{}F_1^{}(\frac{1}{3},\frac{2}{3};1;k^2)$, ${}_2{}^{}F_1^{}(\frac{1}{4},\frac{3}{4};1;k^2)$, and ${}_2{}^{}F_1^{}(\frac{1}{6},\frac{5}{6};1;k^2)$. …

20: 16.23 Mathematical Applications

… ►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.