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Rogers–Fine identity

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11: Bibliography
  • G. E. Andrews (1966b) q -identities of Auluck, Carlitz, and Rogers. Duke Math. J. 33 (3), pp. 575–581.
  • G. E. Andrews (1984) Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.
  • 12: 16.4 Argument Unity
    See Erdélyi et al. (1953a, §4.4(4)) for a non-terminating balanced identity. …
    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
  • R. J. Baxter (1981) Rogers-Ramanujan identities in the hard hexagon model. J. Statist. Phys. 26 (3), pp. 427–452.
  • A. Berkovich and B. M. McCoy (1998) 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.
  • M. V. Berry and F. J. Wright (1980) Phase-space projection identities for diffraction catastrophes. J. Phys. A 13 (1), pp. 149–160.
  • J. M. Borwein and P. B. Borwein (1991) A cubic counterpart of Jacobi’s identity and the AGM. Trans. Amer. Math. Soc. 323 (2), pp. 691–701.
  • J. L. Burchnall and T. W. Chaundy (1948) The hypergeometric identities of Cayley, Orr, and Bailey. Proc. London Math. Soc. (2) 50, pp. 56–74.
  • 14: Guide to Searching the DLMF
    Fine Points in Math Search
    Table 3: A sample of recognized symbols
    Symbols

    Comments

    -=

    For equivalence

    15: Bibliography L
  • J. Lepowsky and S. Milne (1978) Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.
  • J. Lepowsky and R. L. Wilson (1982) A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.
  • 16: 18.33 Polynomials Orthogonal on the Unit Circle
    When a = 0 the Askey case is also known as the Rogers–Szegő case. …
    17: 24.10 Arithmetic Properties
    where m n 0 ( mod p 1 ) . …valid when m n ( mod ( p 1 ) p ) and n 0 ( mod p 1 ) , where ( 0 ) is a fixed integer. …
    24.10.8 N 2 n 0 ( mod p ) ,
    valid for fixed integers ( 1 ) , and for all n ( 1 ) such that 2 n 0 ( mod p 1 ) and p | 2 n .
    24.10.9 E 2 n { 0 ( mod p ) if  p 1 ( mod 4 ) , 2 ( mod p ) if  p 3 ( mod 4 ) ,
    18: 17.1 Special Notation
    Fine (1988) uses F ( a , b ; t : q ) for a particular specialization of a ϕ 1 2 function.
    19: 27.16 Cryptography
    Thus, y x r ( mod n ) and 1 y < n . … By the Euler–Fermat theorem (27.2.8), x ϕ ( n ) 1 ( mod n ) ; hence x t ϕ ( n ) 1 ( mod n ) . But y s x r s x 1 + t ϕ ( n ) x ( mod n ) , so y s is the same as x modulo n . …
    20: 18.1 Notation
    ( z 1 , , z k ; q ) = ( z 1 ; q ) ( z k ; q ) .