# 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

**K. Sushan Bairy**

Department of Mathematics

Bangalore University

Central College Campus

Bengaluru-560 001

INDIA

**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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