# Certain New Modular Identities for Ramanujan's Cubic Continued Fraction

### From NZJM

**New Zealand Journal of Mathematics**

**Vol.** 42, (2012), **Pages** 157-175

**M. S. Mahadeva Naika**

Bangalore University,

Central College Campus,

Bangalore-560 001,

Karnataka,

India

mailto:msmnaika@rediffmail.com

**S. Chandankumar **

Bangalore University,

Central College Campus,

Bangalore-560 001,

Karnataka,

India

**N. P. Suman**

Bangalore University,

Central College Campus,

Bangalore-560 001,

Karnataka,

India

**Abstract** In this paper, first we establish some new relations for ratios of Ramanujan's theta functions. We establish some new general formulas for explicit evaluations of Ramanujan's theta functions. We also establish new relations connecting Ramanujan's cubic continued fraction *V*(*q*) with four other continued fractions *V*(*q*^{15}), *V*(*q*^{5 / 3}), *V*(*q*^{21}) and *V*(*q*^{7 / 3}).

**Keywords** Cubic continued fraction, Modular equations, Theta function.

**Classification** (MSC2000) 33D10, 11A55, 11F27.