Bulletin of the American Mathematical Society

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Book Information

Author(s): George E. Andrews
Title: The theory of partitions
Additional book information: in Encyclopedia of Mathematics and its Applications, volume 2, Addison-Wesley Publishing Company, Advanced Book Program, London, Amsterdam, Don Mills, Ontario, Sydney, and Tokyo, 1976, xiv + 255 pp., $19.50

1.: G. Andrews, An analytic generalization of the Rogers-Ramanujan identities for odd moduli, Proc. Nat. Acad. Sci U.S.A. 71 (1974), 4082-4085. MR 351985
2.: G. Andrews, Problems and prospects for basic hypergeometric functions, Theory and Application of Special Functions (R. Askey, ed.), Academic Press, New York, 1975, pp. 191-224. MR 399528
3.: G. Andrews, q-series and the Lusztig-Macdonald-Wall conjectures, Invent Math. 41 (1977), 91-102. MR 446991
4.: G. Andrews, An introduction to Ramanujan's "lost notebook", Amer. Math. Monthly (to appear).
5.: G. Andrews, Connection coefficient problems and partitions, Proc. Sympos. Pure Math., vol. 34, Amer. Math. Soc. Providence, R. I., 1978, pp. 1-24. MR 525316
6.: G. Andrews and R. Askey, Enumeration of partitions: The role of Eulerian series and q-orthogonal polynomials Higher Combinatorics (M, Aigner, ed.), Reidel, Dordrecht, Holland, 1977, pp. 3-26. MR 519776
7.: P. Appell and E. Lacour, Principes de la théories desfonctions elliptiques, Gauthier-Villars, Paris, 1897.
8.: R. Askey and M. E.-H. Ismail, A generalization of ultraspherical polynomials (to appear in a book dedicated to P. Turán's memory). MR 1801153
9.: R. Bellman, A brief introduction to theta functions, Holt, Rinehart and Winston, New York, 1961. MR 125252
10.: L. Biedenharn and J. Louck, Angular momentum in quantum physics-Theory and application (to appear). MR 635121
11.: D. Bressoud, A new family of partition identities, Pacific J. Math. 77 (1978). MR 506017
12.: D. Bressoud, Combinatorial proof of Schur's theorem (submitted).
13.: D. Bressoud, Extension of the partition sieve (submitted).
14.: D. Bressoud, A generalization of the Rogers-Ramanujan identities for all moduli, J. Combinatorial Theory Ser. A (to appear). MR 541344
15.: D. Bressoud, A functional generalization of the Rogers-Ramanujan identities with interpretation (submitted).
16.: A. Cauchy, Second Mémoire sur les fonctions dont plusieurs valeurs sont liées entre par une équation linéaire, Oeuvres, 1^re Série, Tome VIII, 50-55, Gauthier-Villars, Paris, 1893, reprinted from C. R. 1843.
17.: P. Deligne, La conjecture de Weil. I, Inst Hautes Études Sci Publ. Math. 43 (1974), 273-307. MR 49 #5013. MR 340258
18.: J. Dougall, A theorem of Sonine in Bessel functions, with two extensions to spherical harmonics, Proc. Edinburgh Math. Soc. 37 (1919), 33-47.
19.: F. Dyson, Statistical theory of the energy level of complex systems. I, J. Math. Phys. 3 (1962), 140-156. MR 143556
20.: C. F. Gauss, Disquisitiones generales circa seriem infinitum 1 + αβx/1·γ + α(α + 1)β(β + 1)xx/1·2γ(γ + 1) + ..., Werke, vol. 3, Königlichen Gesellschaft der Wissenschaften, Göttingen, 1866, pp. 123-162 (originally published in 1813).
21.: C. F. Gauss, Zur Theorie der neuen Transscendenten. II, Werke, vol. 3, Göttingen, 1866, pp. 436-445.
22.: C. F. Gauss, Hundert Theoreme über die neuen Transscendenten, Werke, vol. 3, Göttingen, 1866, pp. 461-469.
23.: B. Gordon, A combinatorial generalization of the Rogers-Ramanujan identities, Amer. J. Math. 83 (1961), 393-399. MR 123484
24.: R. W. Gosper, A calculus of series rearrangements, Algorithms and Complexity, New Directions and Recent Results (J. Traub, ed.), Academic Press, New York, 1976, pp. 121-151. MR 451617
25.: G. H. Hardy, Ramanujan, Cambridge Univ. Press, London, 1940; reprinted by Chelsea, New York, 1959. MR 4860
26.: E. Heine, Untersuchungen über die Reihe $1+\frac{(1-q^\alpha)(1-q^\beta)}{(1-q)(1-q^\gamma)}\cdot x+\frac{(1-q^\alpha)(1+q^{\alpha}-1)(1-q^\beta)(1+q^{\beta}-1)}{(1-q)(1-q^2)(1-q^\gamma)(1+q^{\gamma}-1)}\cdot x^2+łdots$ J. Reine Angew Math. 34 (1845), 285-328.
27.: E. Heine, Theorie der Kugelfunctionen und der verwandten Functionen, Reimer, Berlin, 1878.
28.: P. Henrici, Applied and computational complex analysis, vol. 2, Wiley-Interscience, New York, 1977. MR 453984
29.: C. Hermite, Oeuvres, Tome II, Gauthier-Villars, Paris, 1908, pp. 153-156; reprinted from Calcul différentiel et Calcul intégral de Lacroix, 6^e edition, Paris, 1862.
30.: E. Hylleraas, Linearization of products of Jacobi polynomials, Math. Scand. 10 (1962), 189-200. MR 145123
31.: C. G. J. Jacobi, Fundamenta Nova Theoriae Functionum Ellipticarum, Regiomontis, fratrum Bomtraeger 1829; reprinted in Gesammelte Werke, Volume 1, Reimer, Berlin, 1881; reprinted by Chelsea, New York, 1969, pp. 49-239.
32.: I. G. Macdonald, Affine root systems and Dedekind's η-function, Invent. Math. 15 (1972), 91-143. MR 357528
33.: G. Pólya and G. Szegö, Problems and theorems in analysis, vol. I, Springer-Verlag, New York, Heidelberg, Berlin, 1972. MR 396134
34.: G. Racah, Theory of complex spectra. I, II, III, IV, Phys. Rev. 61 (1942), 186-197; 62 (1942), 438-462; 63 (1943), 367-382; 76 (1949), 1352-1365; reprinted in Quantum theory of angular momentum (L. Biedenharn and H. VanDam, ed.), Academic Press, New York, 1965.; 34a. O. Rausenberger, Lehrbuch der Theorie der Periodischen Functionen einer Variabeln, Teubner, Leipzig, 1884.
35.: L. J. Rogers, On a three-fold symmetry in the elements of Heine's series, Proc. London Math. Soc. 24 (1893), 171-179.
36.: L. J. Rogers, On the expansion of some infinite products, Proc. London Math. Soc. 24 (1893), 337-352.
37.: L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
38.: L. J. Rogers, Third memoir on the expansion of certain infinite products, Proc. London Math. Soc. 26 (1895), 15-32.
39.: K. H. Schellbach, Die Lehre von den Elliptischen Integralen und den Theta-Functionen, Reimer, Berlin, 1864.
40.: D. Stanton, Some basic hypergeometric polynomials arising from finite classical groups, Ph.D. thesis, Univ. of Wisconsin, Madison, 1977.
41.: H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms (II), Modular Functions in One Variable V (J.-P. Serre and D. B. Zagier, eds.), Springer-Verlag, Berlin and New York, 1977. MR 406931
42.: J. Wilson, Ph.D. thesis, Univ. of Wisconsin, Madison, 1978.

Review Information:
Journal: Bull. Amer. Math. Soc. 1 (1979), 203-210.
DOI: 10.1090/S0273-0979-1979-14556-7
PII: S 0273-0979(1979)14556-7

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