Mordell integrals and Ramanujan's “lost” notebook

  • George E. Andrews
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 899)


Theta Function Simple Polis Riemann Zeta Function Modular Transformation Mock Theta Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.P. Agarwal, On the paper “A ‘lost’ notebook of Ramanujan I” of G.E. Andrews, Advances in Math., (to appear).Google Scholar
  2. 2.
    G.E. Andrews, On the theorems of Watson and Dragonette for Ramanujan's mock theta functions, Amer. J. Math., 88 (1966), 454–490.MathSciNetCrossRefGoogle Scholar
  3. 3.
    G.E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Vol. 2, G.-C. Rota ed., Addison-Wesley, Reading, 1976.Google Scholar
  4. 4.
    G.E. Andrews, An introduction to Ramanujan's “lost” notebook, Amer. Math. Monthly, 86 (1979), 89–108.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    G.E. Andrews, Ramanujan and his “lost” notebook, Vinculum, 16 (1979), 91–94.Google Scholar
  6. 6.
    G.E. Andrews, Partitions: Yesterday and Today, New Zealand Math. Soc., Wellington, 1979.zbMATHGoogle Scholar
  7. 7.
    G.E. Andrews, Ramanujan's “lost” notebook I: partial theta functions, Advances in Math., (to appear).Google Scholar
  8. 8.
    G.E. Andrews, Ramanujan's “lost” notebook II: θ-function expansions, Advances in Math., (to appear).Google Scholar
  9. 9.
    G.E. Andrews, Ramanujan's “lost” notebook III: the Rogers-Ramanujan continued fraction, Advances in Math., (to appear).Google Scholar
  10. 10.
    W.N. Bailey, On the basic bilateral hypergeometric series 2ψ2, Quart. J. Math., Oxford Ser., 1 (1950), 194–198.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    R. Bellman, A Brief Introduction to Theta Functions, Holt, Rinehart and Winston, New York, 1961.zbMATHGoogle Scholar
  12. 12.
    E.T. Copson, An Introduction to the Theory of Functions of a Complex Variable, Oxford University Press, London, 1935.zbMATHGoogle Scholar
  13. 13.
    L.A. Dragonette, Some asymptotic formulae for the mock theta series of Ramanujan, Amer. J. Math., 72 (1952), 474–500.MathSciNetzbMATHGoogle Scholar
  14. 14.
    C.G.J. Jacobi, Fundamenta Nova Theoriae Functionum Ellipticarum, Regiomonti, fratrum Bornträger, 1829 (Reprinted: in vol. 1, 49–239 of Jacobi's. Gesammelte Werke, Reimer, Berlin 1881–1891, now by Chelsea, New York, 1969).Google Scholar
  15. 15.
    N. Levinson, More than one third of zeros of Riemann's zeta-function are on σ=1/2, Advances in Math., 13 (1974), 383–436.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    L.J. Mordell, The value of the definite integral \(\int_{ - \infty }^\infty {{{e^{at^2 bt} dt} \mathord{\left/{\vphantom {{e^{at^2 bt} dt} {(e^{ct} + d)}}} \right.\kern-\nulldelimiterspace} {(e^{ct} + d)}}}\), Quarterly Journal of Math., 68 (1920), 329–342.Google Scholar
  17. 17.
    L.J. Mordell, The definite integral \(\int_{ - \infty }^\infty {{{e^{ax^2 bx} dx} \mathord{\left/{\vphantom {{e^{ax^2 bx} dx} {(e^{cx} + d)}}} \right.\kern-\nulldelimiterspace} {(e^{cx} + d)}}}\) and the analytic theory of numbers, Acta Math. Stockholm, 61 (1933), 323–360.MathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Ramanujan, Collected Papers, Cambridge University Press, London and New York, 1927; reprinted Chelsea, New York.zbMATHGoogle Scholar
  19. 19.
    D.B. Sears, On the transformation theory of basic hypergeometric functions, Proc. London Math. Soc. (2), 53 (1951), 158–180.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    C.L. Siegel, Über Riemanns Nachlass zur analytischen Zahlentheorie, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, 2 (1933), 45–80.Google Scholar
  21. 21.
    L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, London, 1966.zbMATHGoogle Scholar
  22. 22.
    J. Tannery and J. Molk, Éléments de la Théorie des Fonctions Elliptiques, Vol. II., Gauthier-Villars, Paris, 1896 (Reprinted: Chelsea, New York, 1972).zbMATHGoogle Scholar
  23. 23.
    J. Tannery and J. Molk, Éléments de la Théorie des Fonctions Elliptiques, Vol. III, Gauthier-Villars, Paris 1898 (Reprinted: Chelsea, New York, 1972).zbMATHGoogle Scholar
  24. 24.
    G.N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936), 55–80. *** DIRECT SUPPORT *** A00J4373 00002MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • George E. Andrews
    • 1
  1. 1.The Pennsylvania State UniversityUniversity Park

Personalised recommendations