Ramanujan’s class invariants with applications to the values of 𝑞-continued fractions and theta functions

1997 ◽  
pp. 37-53 ◽  
Author(s):  
Bruce Berndt ◽  
Heng Huat Chan ◽  
Liang-Cheng Zhang
Keyword(s):  
Continued Fractions ◽  
Theta Functions ◽  
Class Invariants

scholarly journals New modular equations of signature three in the spirit of Ramanujan

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2847-2868
Author(s):  
Kumar Srivatsa ◽  
S Shruthi
Keyword(s):  
Theta Function ◽  
Continued Fractions ◽  
Theta Functions ◽  
Modular Equations ◽  
Class Invariants ◽  
Theta Function Identities

Srinivasa Ramanujan recorded many modular equations in his notebooks, which are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature three by using theta function identities of composite degrees.

scholarly journals Modular relations and explicit values of Ramanujan-Selberg continued fractions

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Nayandeep Deka Baruah ◽  
Nipen Saikia
Keyword(s):  
Continued Fractions ◽  
Theta Functions

By employing a method of parameterizations for Ramanujan's theta-functions, we find several modular relations and explicit values of the Ramanujan-Selberg continued fractions.

scholarly journals Generalized Bilateral Eighth Order Mock Theta Functions and Continued Fractions

2019 ◽  
Vol 53 (2) ◽  
pp. 185-193
Author(s):  
Bhaskar Srivastava
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Infinite Product ◽  
Theta Functions ◽  
Generalized Function ◽  
Mock Theta Functions ◽  
Eighth Order ◽  
Independent Variable

We give a two independent variable generalization of bilateral eighth order mock theta functions and expressed them as infinite product. On specializing parameters, we have given a continued fraction representation for the generalized function, which I think is a new representation.

scholarly journals A Note on Continued Fractions and Mock Theta Functions

2016 ◽  
Vol 56 (1) ◽  
pp. 173-184
Author(s):  
Pankaj Srivastava ◽  
Priya Gupta
Keyword(s):  
Continued Fractions ◽  
Theta Functions ◽  
Mock Theta Functions

EXPLICIT EVALUATIONS OF TWO RAMANUJAN–SELBERG CONTINUED FRACTIONS

2005 ◽  
Vol 01 (04) ◽  
pp. 593-601
Author(s):  
LIANG-CHENG ZHANG
Keyword(s):  
Continued Fractions ◽  
Singular Moduli ◽  
Class Invariants

This paper gives explicit evaluations for two Ramanujan–Selberg continued fractions in terms of class invariants and singular moduli.

scholarly journals Some theorems on the explicit evaluation of Ramanujan's theta-functions

2004 ◽  
Vol 2004 (40) ◽  
pp. 2149-2159 ◽  
Author(s):  
Nayandeep Deka Baruah ◽  
P. Bhattacharyya
Keyword(s):  
Continued Fraction ◽  
Theta Functions ◽  
Explicit Evaluation ◽  
Class Invariants

Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants.

scholarly journals Some New Explicit Values of Quotients of Ramanujan’s Theta Functions and Continued Fractions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Nipen Saikia
Keyword(s):  
Continued Fractions ◽  
Theta Functions

We evaluate some new explicit values of quotients of Ramanujan’s theta functions and use them to find explicit values of Ramanujan’s continued fractions.

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