On Level 3 Ramanujan-Sato Type Series for 1/π

Jump To References Section

Authors

  • K. R. Vasuki
     Department of Studies in Mathematics University of Mysore,Manasagangotri, Mysore-570006 ,IN
  • T. Anusha
     School of Cotinuing Education Azim Premji University, Sarjapura, Bengaluru-562125 ,IN
  • H. T. Shwetha
     Department of Mathematics, Vidyavardhaka College of Engineering Mysuru-570002 ,IN

DOI:

https://doi.org/10.18311/jims/2024/36136

Keywords:

Dedekind eta function, Modular equations, Theta Functions, Eisenstein series.

Abstract

Srinivasa Ramanujan developed seventeen fast convergent series for 1/π. Motivated by Ramanujan’s series for 1/π many mathematicians have developed many theories for deriving new series for 1/π. In this article we obtain new series for 1/π using Eisenstein series of level three.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2024-01-01

How to Cite

Vasuki, K. R., Anusha, T., & Shwetha, H. T. (2024). On Level 3 Ramanujan-Sato Type Series for 1/π. The Journal of the Indian Mathematical Society, 91(1-2), 01–09. https://doi.org/10.18311/jims/2024/36136

Issue

Volume 91, Issue 1-2, January-June 2024

Section

Articles

License

Copyright (c) 2024 K. R. Vasuki, T. Anusha, H. T. Shwetha

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

 

References

B. C. Berndt, Ramanujan’s Notebooks, Part II, Springer New York, 1989.

B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer New York, 1991.

H. H. Chan, S. H. Chan, and Z. Liu, Domb’s numbers and Ramanujan-Sato type series for 1/π, Adv. Math, 186 (2004), 396–410.

H. H. Chan, Y. Tanigawa, Y. Yifan, and W. Zudilin, New analogues of clausen’s identities arising from the theory of modular forms, Glasnik Matematicki, 42. (62) (2007), 301-308.

K. R. Vasuki, On certain Ramanujan-Weber type modular equations, J. Indian Math. Soc. (N.S.), 75(1-4) (2009), 173–192.

K. R. Vasuki and K. Shivashankara, A note on explicit evaluations of products and ratios of class invariants, Math. Forum, 13 (1999) , 45–56.

N. D. Baruah, On some of Ramanujan’s Schl¨afli-type “mixed” modular equations., J. Number Theory, 100(2) (2003), 270–294.

R. G. Veeresha, An elementary approach to Ramanujan’s modular equations of degree 7 and its appilications, Doctoral Thesis, University of Mysore, 2015.

S. Cooper , Ramanujan’s Theta Functions, Springer, Cham, 2017.

S. Ramanujan, Modular equations and approximations to π, Quart. J. Math, 45 (1914) ,350–372.

S. Bhargava, K. R. Vasuki, and B. R. S. Kumar, Evaluations of Ramanujan-Weber class invariant gn, J. Indian Math. Soc. (N.S.), 72(1-4) (2005), 115–127.