Rogers–Fine identity
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11—20 of 147 matching pages
11: Bibliography
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-identities of Auluck, Carlitz, and Rogers.
Duke Math. J. 33 (3), pp. 575–581.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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12: 16.4 Argument Unity
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►See Erdélyi et al. (1953a, §4.4(4)) for a non-terminating balanced identity.
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Rogers–Dougall Very Well-Poised Sum
… ►§16.4(iii) Identities
… ►Methods of deriving such identities are given by Bailey (1964), Rainville (1960), Raynal (1979), and Wilson (1978). … ► …13: Bibliography B
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Rogers-Ramanujan identities in the hard hexagon model.
J. Statist. Phys. 26 (3), pp. 427–452.
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Rogers-Ramanujan Identities: A Century of Progress from Mathematics to Physics.
In Proceedings of the International Congress of Mathematicians,
Vol. III (Berlin, 1998),
pp. 163–172.
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Phase-space projection identities for diffraction catastrophes.
J. Phys. A 13 (1), pp. 149–160.
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A cubic counterpart of Jacobi’s identity and the AGM.
Trans. Amer. Math. Soc. 323 (2), pp. 691–701.
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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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14: Guide to Searching the DLMF
15: Bibliography L
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Lie algebraic approaches to classical partition identities.
Adv. in Math. 29 (1), pp. 15–59.
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A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities.
Adv. in Math. 45 (1), pp. 21–72.
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16: 18.33 Polynomials Orthogonal on the Unit Circle
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►When the Askey case is also known as the Rogers–Szegő case.
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17: 24.10 Arithmetic Properties
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►where .
…valid when and , where is a fixed integer.
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24.10.8
►valid for fixed integers , and for all such that
and .
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24.10.9
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18: 17.1 Special Notation
19: 27.16 Cryptography
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►Thus, and .
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►By the Euler–Fermat theorem (27.2.8), ; hence .
But , so is the same as modulo .
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20: 18.1 Notation
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