Ratios of Ramanujan's theta function \psi and evaluations

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New Zealand Journal of Mathematics

Vol. 40, (2010), Pages 33-48


M. S. Mahadeva Naika

Department of Mathematics

Bangalore University

Central College Campus

Bengaluru-560 001

INDIA

mailto:msmnaika@rediffmail.com

S. Chandankumar

Department of Mathematics

Bangalore University

Central College Campus

Bengaluru-560 001

INDIA

mailto:chandan.s17@gmail.com

K. Sushan Bairy

Department of Mathematics

Bangalore University

Central College Campus

Bengaluru-560 001

INDIA

mailto:ksbairy@rediffmail.com


Abstract In this paper, we establish several new modular equations of degree 9 using Ramanujan's mixed modular equations. We also establish several general formulas for explicit evaluations of ratios of Ramanujan's theta function.

Keywords Modular equation, Theta-function

Classification (MSC2000) Primary: 11B65, 33D10, Secondary 11F27.

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