B. R. Srivatsa Kumar, B. Sowmya Navada and Ranjani Nayak

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 1, Pages 86—91

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## Details

### Authors and affiliations

B. R. Srivatsa Kumar

*Department of Mathematics, Manipal Institute of Technology
Manial University, Manipal – 576 104, India*

B. Sowmya Navada

*Department of Sciences, Manipal University
Manipal – 576 104, India*

Ranjani Nayak

*Department of Sciences, Manipal University
Manipal – 576 104, India*

### Abstract

Srinivasa Ramanujan has recorded eleven Schläfli-type mixed modular equations on p. 86 of his first notebook. Using some of these in this paper, we obtain some new identities of the same type by using Maple.

### Keywords

- Theta-functions
- Modular equations

### AMS Classification

- Primary: 11B65, 33D10
- Secondary: 11F27

### References

- Baruah, N. D. (2000) A few theta-function identities and some of Ramanujan’s modular equations, Ramanujan J., 4, 239–250.
- Baruah, N. D. (2003) On some of Ramanujan’s Schläfli-type mixed modular equations, J. Number Theory 100, 270–294. doi:10.1016/S0022-314X(02)00127-0.
- Berndt, B. C. (1991) Ramanujan’s Notebooks, Part III, Springer-Verlag, New York.
- Berndt, B. C. (1998) Ramanujan’s Notebooks, Part V, Springer-Verlag, New York.
- Ramanujan, S. Notebook’s (2 Volumes), Tata Institute of Fundamental Research, Bombay.
- Schläfli, L. (1870) Beweis der Hermiteschen Verwandlungstateln für elliptischen modular function, J. Reine Angew. Math. 72, 360–369.
- Vasuki, K. R. & T. G. Sreeramamurthy. (2005) Certain new Ramanujan’s Schläfli-type mixed modular equations. J. of Mathematical Analysis and Computation, 309, 238–255. doi:10.1016/j.jmaa.2005.01.035.

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## Cite this paper

APASrivatsa Kumar, B. R., Sowmya Navada, B., & Nayak, R. (2015). Some identities on Schläfli-type mixed modular equations. Notes on Number Theory and Discrete Mathematics, 21(1), 86-91.

ChicagoSrivatsa Kumar, B. R., B. Sowmya Navada, and Ranjani Nayak. “Some Identities on Schläfli-type Mixed Modular Equations.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 86-91.

MLASrivatsa Kumar, B. R., B. Sowmya Navada, and Ranjani Nayak. “Some Identities on Schläfli-type Mixed Modular Equations.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 86-91. Print.