Browse > Article
http://dx.doi.org/10.7468/jksmeb.2021.28.1.27

EVALUATIONS OF THE CUBIC CONTINUED FRACTION BY SOME THETA FUNCTION IDENTITIES: REVISITED  

Paek, Dae Hyun (Department of Mathematics Education, Busan National University of Education)
Publication Information
The Pure and Applied Mathematics / v.28, no.1, 2021 , pp. 27-42 More about this Journal
Abstract
In this paper, we exploit some known theta function identities involving two parameters ��k,n and ��′k,n for the theta function �� to find about 54 new values of the Ramanujan's cubic continued fraction.
Keywords
cubic continued fraction; modular equations; theta function identities;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C. Adiga, T. Kim, M.S. Mahadeva Naika & H.S. Madhusudhan: On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions. Indian J. pure appl. Math. 35 (2004), no. 9, 1047-1062.
2 C. Adiga, K.R. Vasuki & M.S. Mahadeva Naika: Some new explicit evaluations of Ramanujan's cubic continued fraction. New Zealand J. Math. 31(2002), 109-114.
3 G.E. Andrews & B.C. Berndt: Ramanujan's lost notebooks, Part I. Springer, 2000
4 B.C. Berndt: Ramanujan's notebooks, Part III. Springer-Verlag, New York, 1991.
5 B.C. Berndt, H.H. Chan & L.-C. Zhang: Ramanujan's class invariants and cubic continued fraction. Acta Arith. 73 (1995), 67-85.   DOI
6 H.H. Chan: On Ramanujan's cubic continued fraction. Acta Arith. 73 (1995), 343-355.   DOI
7 D.H. Paek & J. Yi: On some modular equations and their applications II. Bull. Korean Math. Soc. 50 (2013), no. 4, 1211-1233.
8 D.H. Paek & J. Yi: On evaluations of the cubic continued fraction by modular equations of degree 9. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 23 (2016), no. 3, 223-236.
9 D.H. Paek & J. Yi: On evaluations of the cubic continued fraction by modular equations of degree 3. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (2018), no. 1, 17-29.
10 K.G. Ramanathan: On Ramanujan's continued fraction. Acta Arith. 43 (1984), 209-226.   DOI
11 J. Yi: The construction and applications of modular equations. Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2001.
12 J. Yi, M.G. Cho, J.H. Kim, S.H. Lee, J.M. Yu & D.H. Paek: On some modular equations and their applications I. Bull. Korean Math. Soc. 50 (2013), no. 3, 761-776.   DOI
13 J. Yi, Y. Lee & D.H. Paek: The explicit formulas and evaluations of Ramanujan's theta-function ψ. J. Math. Anal. Appl. 321 (2006), 157-181.   DOI
14 J. Yi & D. H. Paek: Evaluations of the cubic continued fraction by some theta function identities. Korean J. Math. 27 (2019), no. 4, 1043-1059.   DOI