Ramanujan's Theories of Theta and Elliptic Functions


Elliptic Function Theta Function Product Identity Summation Formula Jacobian Elliptic Function 
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  1. Adiga, C., Berndt, B.C., Bhargava, S. and Watson, G.N. (1985). Chapter 16 of Ramanujan’s second notebook: Theta functions and q-series, Memoirs Amer. Math.Soc., No. 315, 53, American Mathematical Society, Providence.Google Scholar
  2. Berndt, B.C. (1985). Ramanujan’s Notebooks, Part III, Springer-Verlag, New York.Google Scholar
  3. Berndt, B.C., Bhargava, S and Garvan, F.G. (1995). Ramanujan’s theories of elliptic functions to alternative bases, Trans. Amer. Math. Soc., 347, 4163–4244.MATHCrossRefMathSciNetGoogle Scholar
  4. Bhargava, S. (1995). Unification of the cubic analogues of the Jacobian Theta-function, J. Math. Anal. Appl., 193, 543–558.MATHCrossRefMathSciNetGoogle Scholar
  5. Bhargava, S. and Fathima, S.N. (2003). Laurent coefficients for cubic theta-functions, South East Asian J. Math. and Math. Sc., 1, 27–31.MATHMathSciNetGoogle Scholar
  6. Bhargava, and Fathima, S.N. (2004). Unification of modular transformations for cubic theta functions, New Zealand J. Math., 33, 121–127.MATHMathSciNetGoogle Scholar
  7. Borwein, J.M., Borwein, P.B. and Garvan, F.G. (1994). Some cubic identities of Ramanujan, Trans. Amer. Math. Soc., 343, 35–37.MATHCrossRefMathSciNetGoogle Scholar
  8. Chan, H.H. (1995). On Ramanujan’s cubic continued fraction, Acta Arithmetica, LXXIII A, 343–355.Google Scholar
  9. Cooper, S. (2003). Cubic theta-functions, J. Comp. Appl. Math., 160, 77–94.MATHCrossRefADSGoogle Scholar
  10. Hirschhorn, M., Garvan F. and Borwein, J. Cubic analogues of the Jacobian theta-function θ(z,q). Google Scholar
  11. Ramanujan, S. (1957). Ramanujan’s Second notebook, TIFR, Bombay.Google Scholar

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