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11: 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. …

12: 17.18 Methods of Computation

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

13: 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). …

14: 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. …

15: 1.1 Special Notation

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$x,y$	real variables.
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$𝐈$	identity matrix
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16: 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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17: 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 ${}_2{}^{}F_1^{}(\frac{1}{6},\frac{5}{6};1;k^2)$. …

18: 21.7 Riemann Surfaces

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§21.7(ii) Fay’s Trisecant Identity

… ►where again all integration paths are identical for all components. Generalizations of this identity are given in Fay (1973, Chapter 2). … ►

§21.7(iii) Frobenius’ Identity

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19: 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.

20: 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. …