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The Fourth and Eighth Order Mock Theta Functions
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  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 1,  2010, pp.165-175
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.1.165
 Title & Authors
The Fourth and Eighth Order Mock Theta Functions
Srivastava, Bhaskar;
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In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to . I presume they will be helpful in getting fundamental transformations.
Mock theta functions;Basic hypergeometric series;Bailey pair;
 Cited by
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G. E. Andrews and D. Hickerson, Ramanujan's " Lost" Notebook VII: The sixth order mock theta functions, Adv. in Math., 89(1991), 60-105. crossref(new window)

D. Hickerson, A proof of mock theta conjectures, Inven. Math., 94(1998), 639-660.

D. Hickerson, On the seventh order mock theta functions, Inven. Math., 94(1988), 661-677. crossref(new window)

K. Hikami, Mock (false) theta functions as quantum invariants, Regular and Chaotic Dynamics, 10(2005), 509-530. crossref(new window)

S. Ramanujan, Collected Papers, Cambridge University Press, 1927, reprinted Chelsea, New York, 1962.

G. N. Watson, The final problem: An account of the mock theta functions, J. London Math. Soc., 11(1936), 55-80. crossref(new window)

S. Zwegers, On two fifth order mock theta functions, The Ramanujan Journal, (accepted)