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
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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
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