Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지

Ramanujan's Continued Fraction, a Generalization and Partitions

  • Received : 2004.03.17
  • Published : 2005.06.23
Download PDF
⟨ Previous Next ⟩

Abstract

We generalize a continued fraction of Ramanujan by introducing a free parameter. We give the closed form for the continued fraction. We also consider the finite form giving $n^{th}$ convergent using partition theory.

Keywords

References

  1. Quart. J. Math. (Oxford) v.19 On q-difference equations for certain well-poised basic hypergeometric series Andrews, G.E.
  2. Duke Math. J. v.39 Some continued fraction formulas Carlitz, L.
  3. Basic Hypergeometric Series Gasper, G.;Rahman, M.
  4. Duke Math. J. v.39 Partitions and Ramanujan's continued fraction Hirschhorn, M.D.
  5. J. Australian Math. Soc. v.29 A continued fraction of Ramanujan Hirschhorn, M.D.
  6. Combinatory Analysis MacMohan, P.A.
  7. Collected Papers Ramanujan, S.
  8. Proc. London Math. Soc. v.54 Further identities of the Rogers-Ramanujan type Slater, L.J.