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1: 17.18 Methods of Computation
Lehner (1941) uses Method (2) in connection with the RogersRamanujan 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: Bibliography
  • G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen (1992a) Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.
  • G. E. Andrews (1966b) q -identities of Auluck, Carlitz, and Rogers. Duke Math. J. 33 (3), pp. 575–581.
  • G. E. Andrews (1972) Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.
  • G. E. Andrews (1984) Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.
  • M. J. Atia, A. Martínez-Finkelshtein, P. Martínez-González, and F. Thabet (2014) Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters. J. Math. Anal. Appl. 416 (1), pp. 52–80.
  • 4: 17.12 Bailey Pairs
    The Bailey pair that implies the RogersRamanujan identities §17.2(vi) is: …
    5: 17.14 Constant Term Identities
    §17.14 Constant Term Identities
    RogersRamanujan Constant Term Identities
    6: 26.10 Integer Partitions: Other Restrictions
    The set { n 1 | n ± j ( mod k ) } is denoted by A j , k . …
    Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from A j , k .
    p ( 𝒟 , n ) p ( 𝒟 2 , n ) p ( 𝒟 2 , T , n ) p ( 𝒟 3 , n )
    20 64 31 20 18
    §26.10(iv) Identities
    Equations (26.10.13) and (26.10.14) are the RogersRamanujan identities. …
    7: Bibliography R
  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
  • S. Ramanujan (1962) Collected Papers of Srinivasa Ramanujan. Chelsea Publishing Co., New York.
  • 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: 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.
  • B. C. Berndt (1989) Ramanujan’s Notebooks. Part II. Springer-Verlag, New York.
  • B. C. Berndt (1991) Ramanujan’s Notebooks. Part III. Springer-Verlag, Berlin-New York.
  • I. Bloch, M. H. Hull, A. A. Broyles, W. G. Bouricius, B. E. Freeman, and G. Breit (1950) Methods of calculation of radial wave functions and new tables of Coulomb functions. Physical Rev. (2) 80, pp. 553–560.
  • 9: Bibliography L
  • D. F. Lawden (1989) Elliptic Functions and Applications. Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.
  • D. H. Lehmer (1943) Ramanujan’s function τ ( n ) . Duke Math. J. 10 (3), pp. 483–492.
  • D. H. Lehmer (1947) The vanishing of Ramanujan’s function τ ( n ) . Duke Math. J. 14 (2), pp. 429–433.
  • 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.
  • 10: 17.2 Calculus
    §17.2(vi) RogersRamanujan Identities
    These identities are the first in a large collection of similar results. …