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.

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

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 Second-order integrable Lagrangians and WDVV equations

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue
Keyword(s):  
Lagrangian Density ◽  
Theta Functions ◽  
Second Order ◽  
Elementary Functions ◽  
Lagrange Equations ◽  
Wdvv Equations ◽  
Integrability Conditions ◽  
Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

scholarly journals Higher depth mock theta functions and q-hypergeometric series

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Joshua Males ◽  
Andreas Mono ◽  
Larry Rolen
Keyword(s):  
Theta Function ◽  
Modular Forms ◽  
Hypergeometric Series ◽  
Theta Functions ◽  
Mock Theta Function ◽  
Mock Theta Functions ◽  
Maass Forms ◽  
Mock Modular Forms ◽  
Harmonic Maass Forms

Abstract In the theory of harmonic Maaß forms and mock modular forms, mock theta functions are distinguished examples which arose from q-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms, which we call higher depth mock theta functions, and develop q-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a q-hypergeometric series.

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