A continued fraction of order twelve

• Autorzy: M. Mahadeva Naika , B. Dharmendra , K. Shivashankara
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

continued fraction; modular equation; reciprocity theorem

Kategorie tematyczne

• 11F55: Other groups and their modular and automorphic forms (several variables)
• 11S23: Integral representations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 3
• Strony: 393-404

Daty

wydano

2008-09-01

online

2008-07-02

Twórcy

autor

M. Mahadeva Naika

• Bangalore University, Central College Campus

autor

B. Dharmendra

• Bangalore University, Central College Campus

autor

K. Shivashankara

• Yuvaraja’s College, University of Mysore

Bibliografia

• [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
• [2] Berndt B.C., Ramanujan’s notebooks Part III, Springer-Verlag, New York, 1991
• [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

Identyfikatory

DOI

10.2478/s11533-008-0031-y