Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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General Theorem for Explicit Evaluations and Reciprocity Theorems for Ramanujan-Göllnitz-Gordon Continued Fraction

  • SAIKIA, NIPEN (Department of Mathematics, Rajiv Gandhi University)
  • Received : 2014.02.13
  • Accepted : 2014.08.21
  • Published : 2015.12.23
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Abstract

In the paper A new parameter for Ramanujan's theta-functions and explicit values, Arab J. Math. Sc., 18 (2012), 105-119, Saikia studied the parameter $A_{k,n}$ involving Ramanujan's theta-functions ${\phi}(q)$ and ${\psi}(q)$ for any positive real numbers k and n and applied it to find explicit values of ${\psi}(q)$. As more application to the parameter $A_{k,n}$, in this paper we prove a new general theorem for explicit evaluation of Ramanujan-$G{\ddot{o}}llnitz$-Gordon continued fraction K(q) in terms of the parameter $A_{k,n}$ and give examples. We also find some new explicit values of the parameter $A_{k,n}$ and offer reciprocity theorems for the continued fraction K(q).

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References

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Cited by

  1. New theta-function identities and general theorems for the explicit evaluations of Ramanujan’s continued fractions vol.5, pp.3, 2016, https://doi.org/10.1007/s40065-016-0149-x