q-Orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions

George E. Andrews1
1Department of Mathematics, The Pennsylvania State University, University Park, USA

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Tài liệu tham khảo

G. E. Andrews, The Theory of Partitions (Addison-Wesley, Reading, MA, 1976; Cambridge Univ. Press, Cambridge, 1984), Encycl. Math. Appl. 2.

G. E. Andrews, “Multiple Series Rogers-Ramanujan Type Identities,” Pac. J. Math. 114, 267–283 (1984).

G. E. Andrews, “The Fifth and Seventh Order Mock Theta Functions,” Trans. Am. Math. Soc. 293, 113–134 (1986).

G. E. Andrews, q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra (Am. Math. Soc., Providence, RI, 1986), CBMS Reg. Conf. Ser. Math. 66.

G. E. Andrews, “Parity in Partition Identities,” Ramanujan J. 23, 45–90 (2010).

G. E. Andrews, “Partitions with Early Conditions” (to appear).

G. E. Andrews and R. Askey, “Enumeration of Partitions: The Role of Eulerian Series and q-Orthogonal Polynomials,” in Higher Combinatorics: Proc. NATO Adv. Study Inst., Berlin, 1976, Ed. by M. Aigner (D. Reidel, Boston, 1977), pp. 3–26.

G. E. Andrews, R. Askey, and R. Roy, Special Functions (Cambridge Univ. Press, Cambridge, 1999), Encycl. Math. Appl. 71.

G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook (Springer, New York, 2009), Part II.

G. E. Andrews, F. J. Dyson, and D. Hickerson, “Partitions and Indefinite Quadratic Forms,” Invent. Math. 91, 391–407 (1988).

G. E. Andrews and D. Hickerson, “Ramanujan’s “Lost” Notebook. VII: The Sixth Order Mock Theta Functions,” Adv. Math. 89, 60–105 (1991).

F. C. Auluck, “On Some New Types of Partitions Associated with Generalized Ferrers Graphs,” Proc. Cambridge Philos. Soc. 47, 679–686 (1951).

W. N. Bailey, “Some Identities in Combinatory Analysis,” Proc. London Math. Soc., Ser. 2,49, 421–435 (1947).

W. N. Bailey, “Identities of the Rogers-Ramanujan Type,” Proc. London Math. Soc., Ser. 2,50, 1–10 (1948).

W. N. Bailey, “On the Simplification of Some Identities of the Rogers-Ramanujan Type,” Proc. London Math. Soc., Ser. 3,1, 217–221 (1951).

N. J. Fine, Basic Hypergeometric Series and Applications (Am. Math. Soc., Providence, RI, 1988), Math. Surv. Monogr. 27.

G. Gasper and M. Rahman, Basic Hypergeometric Series (Cambridge Univ. Press, Cambridge, 1990), Encycl. Math. Appl. 35.

L. J. Slater, “Further Identities of the Rogers-Ramanujan Type,” Proc. London Math. Soc., Ser. 2, 54, 147–167 (1952).

G. N. Watson, “A New Proof of the Rogers-Ramanujan Identities,” J. London Math. Soc. 4, 4–9 (1929).

G. N. Watson, “The Final Problem: An Account of the Mock Theta Functions,” J. London Math. Soc. 11, 55–80 (1936).