# A continued fraction of order twelve

M. Mahadeva Naika; B. Dharmendra; K. Shivashankara

Open Mathematics (2008)

- Volume: 6, Issue: 3, page 393-404
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topM. Mahadeva Naika, B. Dharmendra, and K. Shivashankara. "A continued fraction of order twelve." Open Mathematics 6.3 (2008): 393-404. <http://eudml.org/doc/269355>.

@article{M2008,

abstract = {In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.},

author = {M. Mahadeva Naika, B. Dharmendra, K. Shivashankara},

journal = {Open Mathematics},

keywords = {continued fraction; modular equation; reciprocity theorem},

language = {eng},

number = {3},

pages = {393-404},

title = {A continued fraction of order twelve},

url = {http://eudml.org/doc/269355},

volume = {6},

year = {2008},

}

TY - JOUR

AU - M. Mahadeva Naika

AU - B. Dharmendra

AU - K. Shivashankara

TI - A continued fraction of order twelve

JO - Open Mathematics

PY - 2008

VL - 6

IS - 3

SP - 393

EP - 404

AB - In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

LA - eng

KW - continued fraction; modular equation; reciprocity theorem

UR - http://eudml.org/doc/269355

ER -

## References

top- [1] Adiga C., Berndt B.C., Bhargava S., Watson G.N., Chapter 16 of Ramanujan’s second notebook: theta-function and q-series, Mem. Amer. Math. Soc., 1985, 53, no. 315 Zbl0565.33002
- [2] Berndt B.C., Ramanujan’s notebooks Part III, Springer-Verlag, New York, 1991 Zbl0733.11001
- [3] Chan H.H., Ramanujan’s elliptic functions to alternative bases and approximations to π, Number Theory for the Millennium I, Proceedings of the Millennial Number Theory Conference (May 2000 Champaign-Urbana USA), 2002, 197–213
- [4] Jacobsen L., Domains of validity for some of Ramanujan’s continued fraction formulas, J. Math. Anal. Appl., 1989, 143, 412–437 http://dx.doi.org/10.1016/0022-247X(89)90049-8
- [5] Ramanujan S., Notebooks, Tata Institute of Fundamental Research, Bombay, 1957

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.