The Journal of the Indian Mathematical Society

K. R. Vasuki ¹, G. Sharath ¹

Affiliations
1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570 006, IN

Abstract

On page 309 of his second notebook, Ramanujan has recorded a modular equation of composite degree 1, 3, 9, 27. B. C. Berndt has dis-proved the same and did not mention the correct one. The purpose of this paper is to establish the same.

Keywords

Theta Functions, Modular Equations.

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K. R. Vasuki ¹, K. Shivashankara ²

Affiliations
1 Department of Mathematics, Acharya Institute of Technology, Soldevanahalli, Chikkabanavara (Post), Hesaragatta Road, Bangalore-560090, IN
2 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570006, IN

Abstract

In his first and lost notebooks, Ramanujan has recorded several values for the Rogers-Ramanujan continued fraction. B.C. Berndt, H.H. Chan and L.-C. Zhang have established all these values on employing some of Ramanujan’s eta-function identities. In this paper we obtain some new values for the Rogers-Ramanujan continued fraction.

Keywords

Theta Functions, Rogers-Ramanujan Continued Fraction.

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S. Bhargava , K. R. Vasuki ¹, B. R. Srivatsa Kumar ¹

Affiliations
1 Department of Mathematics, Acharya Institute of Technology, Soldevanahalli Chikkabanavara (Post), Hesaraghatta Road, Bangalore-560 090, IN

Abstract

By employing P - Q eta function identities involving 4 arguments, we establish several values of the class invariant g_n

Keywords

Eta Function Identities, Class Invariants.

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