Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: https://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(3), 90-95
DOI: 10.12691/tjant-2-3-7
Open AccessArticle

New Properties for The Ramanujan’S Continued Fraction of Order 12

Chandrashekar Adiga1, , M. S. Surekha1 and A. Vanitha1

1Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, INDIA

Pub. Date: July 03, 2014

Cite this paper:
Chandrashekar Adiga, M. S. Surekha and A. Vanitha. New Properties for The Ramanujan’S Continued Fraction of Order 12. Turkish Journal of Analysis and Number Theory. 2014; 2(3):90-95. doi: 10.12691/tjant-2-3-7

Abstract

In this paper, we derive new identities involving a continued fraction of Ramanujan of order twelve that are similar to those of the Ramanujan-Göllnitz-Gordon continued fraction.

Keywords:
continued fraction power series expansion

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References:

[1]  C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Chapter 16 of Ramanujan’s second notebook: Theta functions and q-series, Mem. Amer. Math. Soc.,315 (1985), 1-91.
 
[2]  C. Adiga, K. R. Vasuki and N. Bhaskar, Some new modular relations for the cubic functions, South East Asian Bull. Math.,36 (2012), 1-19.
 
[3]  G. E. Andrews, On q- difference equations for certain well-poised basic hyoergeometric series, Quart. J. Math. (Oxford),19 (1968), 433-447.
 
[4]  N. D. Baruah and R. Barman, Certain theta function identities and Ramanujan’s modular equations of degree 3, Indian J. Math.,48 (3) (2006), 113-133.
 
[5]  B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.
 
[6]  S. Bhargava, C. Adiga and D. D. Somashekara, Ramanujan’s remarkable summation formula and an interesting convolution identity, Bull. Austral. Math. Soc.,47 (1993), 155-162.
 
[7]  Boonrod Yuttanan, New properties for the Ramanujan-Göllnitz-Gordon continued fraction, Acta Arithmetric, 151(3) (2012), 293-310.
 
[8]  H. Göllnitz, Partitionen mit Diffrenzenbedinguggen, J. Reine Angew Math, 225 (1967), 154-190.
 
[9]  B. Gordon, Some continued fractions of the Rogers-Ramanujan type, Duke Math. J.32 (1965), 741-748.
 
[10]  M. S. Mahadeva Naika, B. N. Dharmendra and K. Shivashankar, A continued fraction of order twelve, Centr. Eur. J. Math.,6 (3) (2008), 393-404.
 
[11]  S. Ramanujan, Notebooks (2 volumes), Tata Inst. Fund. Res., Bombay, 1957.
 
[12]  H. M. Srivastava, Some convolution identities based upon Ramanujan’s bilateral sum, Bull. Austral. Math. Soc.,49 (1994), 433-437.
 
[13]  K. R. Vasuki, Abdulrawf A. Kahtan, G. Sharth and C. Sathish Kumar, On a continued fraction of order 12, Ukra. Math. J.,62 (12) (2010), 1866-1878.
 
[14]  K. R. Vasuki, G. Sharth and K. R. Rajanna, Two modular equations for squares of the cubic functions with applications, Note di Math.30 (2) (2010), 61-70.
 
[15]  K. W. Yang, On the product , J.Austral. Math. Soc., Ser.A 48 (1990), 148-151.