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Explicit evaluations of Ramanujan's remarkable product of theta-function

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Abstract

On pages 338 and 339 in his first notebook [9], Ramanujan records eighteen values for a certain product of theta-function. All these have been proved by B. C. Berndt,H. Chan and L-C. Zhang [7]. The main purpose of this paper is to establish several new explicit evaluations of Ramanujan’s remarkable product of theta-function.

참고문헌 (9)

  1. Adiga, C., "Chapter 16 of Ramanujan’s second notebook: Theta-function and q-series", Mem. Amer. Math. Soc., 53(315) (1985), Amer. Math. Soc., Providence
  2. Berndt, B. C., "Ramanujan’s Notebooks, Part III" (1991), Springer-Verlag, New York
  3. Berndt, B. C., "Ramanujan’s Notebooks, Part IV" (1994), Springer-Verlag, New York
  4. Berndt, B. C., "Ramanujan’s Notebooks, Part V" (1998), Springer-Verlag, New York
  5. Berndt, B. C., "Ramanujan’s remarkable product of the theta-function", Proc. Edinburgh Math. soc., 40, pp.583~612 (1997)
  6. Borwein, J. M., "Pi and AGM" (1987), Wiley, New York
  7. Naika, M. S. Mahadeva, "P −Q eta-function identities and computations of Ramanujan-Weber class invariants", The J. Indian Math. soc., 70 (2003)
  8. Naika, M. S. Mahadeva, "On some new general theorems for the explicit evaluations of Ramanujan’s remarkable product of theta-function", The Ramanujan Journal
  9. Ramanujan, S., "Notebooks, 2 volumes" (1957), Tata Institute of Fundamental Research, Bombay

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