Pacific Journal of Mathematics

Multiple series Rogers-Ramanujan type identities.

George E. Andrews

Article information

Source
Pacific J. Math. Volume 114, Number 2 (1984), 267-283.

Dates
First available: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102708707

Zentralblatt MATH identifier
0547.10012

Mathematical Reviews number (MathSciNet)
MR757501

Subjects
Primary: 11P80
Secondary: 05A19: Combinatorial identities, bijective combinatorics 05A30: $q$-calculus and related topics [See also 33Dxx]

Citation

Andrews, George E. Multiple series Rogers-Ramanujan type identities. Pacific Journal of Mathematics 114 (1984), no. 2, 267--283. http://projecteuclid.org/euclid.pjm/1102708707.


Export citation

References

  • [I] R. P. Agarwal, On the partial sums of series of hypergeometric type, Proc. Cambridge Phil. Soc, 49 (1953), 441-445.
  • [2] G. E. Andrews, A polynomial identity which implies the Rogers-Ramanujan identities, Scripta Math., 28 (1970), 297-305.
  • [3] G. E. Andrews, Applications of basic hypergeometric functions, S.I.A.M. Review, 16 (1974), 441-484.
  • [4] G. E. Andrews, An analytic generalization of the Rogers-Ramanuj an identities for odd moduli, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 4082-4085.
  • [5] G. E. Andrews, Problems and Prospects for Basic Hypergeometric Functions, The Theory and Applications of Special Functions, (R. Askey, ed.), Academic Press, New York, 1975, pp. 191-224.
  • [6] G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Vol. 2, Addison-Wesley, 1976.
  • [7] G. E. Andrews, Connection coefficient problems and partitions, Relations Between Combinator- ics and Other Parts of Mathematics, D. K. Ray-Chaudhuri ed., Proc. Symp. Pure Math, 34 (1979), 1-24.
  • [8] G. E. Andrews, Partitions and Durfee dissection, Amer. J. Math, 101 (1979), 735-742.
  • [9] G. E. Andrews, The hard-hexagon model and Rogers-Ramanuj an type identities, Proc. Nat. Acad. Sci. U.S.A., 78 (1981), 5290-5292.
  • [10] G. E. Andrews, On the Wall polynomials and the L-M-W conjectures, J. Austral. Math. Soc. (to appear).
  • [II] G. E. Andrews and R. Askey, Enumeration of partitions: the role of Eulerian series and q-orthogonal polynomials, from Higher Combinatorics, M. Aigner ed, Reidel, Dordrecht, 1977, pp. 3-26.
  • [12] W. N. Bailey, Some identities in combinatory analysis, Proc. London Math. Soc, (2), 49 (1947), 421-435.
  • [13] W. N. Bailey, Identities of the Rogers-Ramanuj an type, Proc. London Math. Soc, (2), 50 (1949), 1-10.
  • [14] D. M. Bressoud, Analytic and combinatorial generalizations of the Rogers-Ramanuj an identities, Memoirs Amer. Math. Soc, 24 (1980), No. 227, 54 pp.
  • [15] D. M. Bressoud, Some identities for terminating q-series, Math. Proc. Camb. Phil. Soc, 89 (1981), 211-223.
  • [16] F. H. Jackson, Examples of a generalization of Euler's transformation for power series, Messenger of Math, 57 (1928), 169-187.
  • [17] S. Milne, A generalization of Andrews' reduction formula for the Rogers-Selberg functions, Amer. J. Math, 104 (1982), 635-643.
  • [18] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc, 25 (1894), 318-343.
  • [19] L. J. Rogers, On two theorems of combinatory analysis and some allied identities, Proc. London Math. Soc, (2), 16 (1917), 315-336.
  • [20] L. J. Rogers and S. Ramanujan, Proof of certain identities in combinatory analysis, Proc. Camb. Phil. Soc, 19 (1919), 211-214.
  • [21] I. Schur, Ein Beitrag zur additien Zahlentheorie und zur Theore der Kettenbriche, Sitz.-Ber. Preuss. Akad. Wiss. Phys.-Math. KL, 1917, pp. 302-321. (Reprinted in I. Schur, Gesammelte Abhandlungen, Vol. 2, pp. 117-136, Springer, Berlin,1973).
  • [22] L. J. Slater, A new proof of Rogers's transformations of infinite series, Proc. London Math. Soc. (2),53 (1951),460-475.
  • [23] L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2), 54 (1952), 147-167.
  • [24] L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, London and New York, 1966.
  • [25] A. Verma and V. K. Jain, Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type, J. Math. Analysis and Appl., 76 (1980),230-269.
  • [26] A. Verma and V. K. Jain, Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identities, J. Math. Analysis and Appl., 87 (1982), 9-44.
  • [27] G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Australian Math. Soc,3 (1963), 1-62.
  • [28] G. N. Watson, A new proof of the Rogers-Ramanujan identities, J. London Math. Soc, 4 (1929), 4-9.