Certain New Modular Identities for Ramanujan's Cubic Continued Fraction

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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

mailto:chandan.s17@gmail.com

N. P. Suman

Bangalore University,

Central College Campus,

Bangalore-560 001,

Karnataka,

India

mailto:npsuman.13@gmail.com


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(q15), V(q5 / 3), V(q21) and V(q7 / 3).

Keywords Cubic continued fraction, Modular equations, Theta function.

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

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