Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.P. Agarwal, On the paper “A ‘lost’ notebook of Ramanujan I” of G.E. Andrews, Advances in Math., (to appear).
G.E. Andrews, On the theorems of Watson and Dragonette for Ramanujan's mock theta functions, Amer. J. Math., 88 (1966), 454–490.
G.E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Vol. 2, G.-C. Rota ed., Addison-Wesley, Reading, 1976.
G.E. Andrews, An introduction to Ramanujan's “lost” notebook, Amer. Math. Monthly, 86 (1979), 89–108.
G.E. Andrews, Ramanujan and his “lost” notebook, Vinculum, 16 (1979), 91–94.
G.E. Andrews, Partitions: Yesterday and Today, New Zealand Math. Soc., Wellington, 1979.
G.E. Andrews, Ramanujan's “lost” notebook I: partial theta functions, Advances in Math., (to appear).
G.E. Andrews, Ramanujan's “lost” notebook II: θ-function expansions, Advances in Math., (to appear).
G.E. Andrews, Ramanujan's “lost” notebook III: the Rogers-Ramanujan continued fraction, Advances in Math., (to appear).
W.N. Bailey, On the basic bilateral hypergeometric series 2ψ2, Quart. J. Math., Oxford Ser., 1 (1950), 194–198.
R. Bellman, A Brief Introduction to Theta Functions, Holt, Rinehart and Winston, New York, 1961.
E.T. Copson, An Introduction to the Theory of Functions of a Complex Variable, Oxford University Press, London, 1935.
L.A. Dragonette, Some asymptotic formulae for the mock theta series of Ramanujan, Amer. J. Math., 72 (1952), 474–500.
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).
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.
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.
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.
S. Ramanujan, Collected Papers, Cambridge University Press, London and New York, 1927; reprinted Chelsea, New York.
D.B. Sears, On the transformation theory of basic hypergeometric functions, Proc. London Math. Soc. (2), 53 (1951), 158–180.
C.L. Siegel, Über Riemanns Nachlass zur analytischen Zahlentheorie, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, 2 (1933), 45–80.
L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, London, 1966.
J. Tannery and J. Molk, Éléments de la Théorie des Fonctions Elliptiques, Vol. II., Gauthier-Villars, Paris, 1896 (Reprinted: Chelsea, New York, 1972).
J. Tannery and J. Molk, Éléments de la Théorie des Fonctions Elliptiques, Vol. III, Gauthier-Villars, Paris 1898 (Reprinted: Chelsea, New York, 1972).
G.N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936), 55–80. *** DIRECT SUPPORT *** A00J4373 00002
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to an outstanding mathematician and human being, Emil Grosswald
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Andrews, G.E. (1981). Mordell integrals and Ramanujan's “lost” notebook. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096452
Download citation
DOI: https://doi.org/10.1007/BFb0096452
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11173-3
Online ISBN: 978-3-540-38953-8
eBook Packages: Springer Book Archive