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Rogers–Fine identity

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1: 17.18 Methods of Computation
Lehner (1941) uses Method (2) in connection with the Rogers–Ramanujan identities. …
2: 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. …
3: 17.12 Bailey Pairs
The Bailey pair that implies the Rogers–Ramanujan identities §17.2(vi) is: …
4: 17.6 ϕ 1 2 Function
Fine’s First Transformation
Fine’s Second Transformation
Fine’s Third Transformation
17.6.11 1 - z 1 - b ϕ 1 2 ( q , a q b q ; q , z ) = n = 0 ( a q ; q ) n ( a z q / b ; q ) 2 n b n ( z q , a q / b ; q ) n - a q n = 0 ( a q ; q ) n ( a z q / b ; q ) 2 n + 1 ( b q ) n ( z q ; q ) n ( a q / b ; q ) n + 1 , | z | < 1 , | b | < 1 .
RogersFine Identity
5: 17.14 Constant Term Identities
§17.14 Constant Term Identities
Rogers–Ramanujan Constant Term Identities
6: 26.10 Integer Partitions: Other Restrictions
The set { n 1 | n ± j ( mod k ) } is denoted by A j , k . …
§26.10(iv) Identities
Equations (26.10.13) and (26.10.14) are the Rogers–Ramanujan identities. …
7: Bibliography R
  • J. Riordan (1979) Combinatorial Identities. Robert E. Krieger Publishing Co., Huntington, NY.
  • M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
  • 8: 17.16 Mathematical Applications
    More recent applications are given in Gasper and Rahman (2004, Chapter 8) and Fine (1988, Chapters 1 and 2).
    9: 17 q-Hypergeometric and Related Functions
    10: 17.2 Calculus
    §17.2(vi) Rogers–Ramanujan Identities
    These identities are the first in a large collection of similar results. …