Somashekara, D. D. and Shalini, S. L. and Narasimha Murthy, K.
(2013)
*On some continued fraction expansions for the ratios of the function ρ(a, b).*
Note di Matematica, 33 (2).
pp. 35-42.
ISSN 1123-2536

Text (Full Text)
Mat_2013_Somashekara.pdf - Published Version Restricted to Registered users only Download (198kB) | Request a copy |

## Abstract

In his lost notebook, Ramanujan has defined the function ρ(a, b) by ρ(a, b) := 1 + 1 b X∞ n=0 (−1)n q n(n+1)/2 a n b −n (−aq)n , where |q| < 1, and (a; q)n = Qn−1 k=0 (1 − aqk ), n = 1, 2, 3, . . . , and has given a beautiful reciprocity theorem involving ρ(a, b). In this paper we obtain some continued fraction expansions for the ratios of ρ(a, b) with some of its contiguous functions. We also obtain some interesting special cases of our continued fraction expansions which are analogous to the continued fraction identities stated by Ramanujan.

Item Type: | Article |
---|---|

Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | Arshiya Kousar Library Assistant |

Date Deposited: | 30 Oct 2019 11:15 |

Last Modified: | 30 Oct 2019 11:15 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/9675 |

### Actions (login required)

View Item |