On the approximation of some special functions in Ramanujan's generalized modular equation with signature \(3^{\ast}\)
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Publication:2240485
DOI10.1007/s11139-021-00437-4zbMath1489.33002OpenAlexW3171054789MaRDI QIDQ2240485
Hong-Hu Chu, Miao-Kun Wang, Yu-Ming Chu
Publication date: 4 November 2021
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-021-00437-4
Gaussian hypergeometric functionRamanujan's cubic transformationgeneralized Grötzsch ring functionRamanujan's generalized modular equation
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On the bounds of the perimeter of an ellipse ⋮ Sharp inequalities for the Toader mean of order -1 in terms of other bivariate means ⋮ On the generalized power-type Toader mean ⋮ Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions ⋮ Dependence on the parameter of generalized Grötzsch ring and generalized Hübner functions ⋮ Sharp bounds for the lemniscatic mean by the one-parameter geometric and quadratic means ⋮ On the monotonicity and convexity for generalized elliptic integral of the first kind
Cites Work
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- Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
- Optimal combinations bounds of root-square and arithmetic means for Toader mean
- Concavity of the complete elliptic integrals of the second kind with respect to Hölder means
- Bounds for complete elliptic integrals of the second kind with applications
- On a theory of elliptic functions based on the incomplete integral of the hypergeometric function \({_{2}}F_{1}(\frac{1}{4},\frac{3}{4};\frac{1}{2};z)\)
- A power mean inequality involving the complete elliptic integrals
- On the modulus of the Grötzsch ring
- A class of logarithmically completely monotonic functions associated with a gamma function
- Logarithmically complete monotonicity properties relating to the gamma function
- Generalized Hersch-Pfluger distortion function and complete elliptic integrals
- On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function
- Monotonicity, convexity, and inequalities involving the Agard distortion function
- Convexity of the complete elliptic integrals of the first kind with respect to Hölder means
- Asymptotical formulas for Gaussian and generalized hypergeometric functions
- Optimal bounds for the generalized Euler-Mascheroni constant
- Inequalities for the generalized elliptic integrals and modular functions
- Ramanujan's cubic transformation and generalized modular equation
- Cubic modular equations in two variables
- Convexity with respect to Hölder mean involving zero-balanced hypergeometric functions
- A double inequality for gamma function
- Monotonic and logarithmically convex properties of a function involving gamma functions
- Generalized elliptic integrals and modular equations
- Inequalities and infinite product formula for Ramanujan generalized modular equation function
- On the generalized modulus
- Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters
- On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
- Refinements of transformation inequalities for zero-balanced hypergeometric functions
- Optimal Lehmer mean bounds for the Toader mean
- A note on Ramanujan's identities involving the hypergeometric function \({_{2}}F_{1}(\frac{1}{6},\frac{5}{6};1;z)\)
- Asymptotical bounds for complete elliptic integrals of the second kind
- Monotonicity criterion for the quotient of power series with applications
- Generalized elliptic integrals
- On rational bounds for the gamma function
- An optimal power mean inequality for the complete elliptic integrals
- Cubic theta functions
- Level 14 and 15 analogues of Ramanujan’s elliptic functions to alternative bases
- A power mean inequality for the Grötzsch ring function
- Singular values, Ramanujan modular equations, and Landen transformations
- Hölder mean inequalities for the complete elliptic integrals
- Some inequalities for the generalized distortion functions
- Hölder mean inequalities for the generalized Grötzsch ring and Hersch-Pfluger distortion functions
- Remarks on generalized elliptic integrals
- Topics in Special Functions
- A monotonicity property involving the generalized elliptic integral of the first kind
- Sharp Gautschi inequality for parameter 0<p<1 with applications
- On approximating the error function
- Landen inequalities for a class of hypergeometric functions with applications
- Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function
- Infinite Products and Normalized Quotients of Hypergeometric Functions
- Ramanujan's Theories of Elliptic Functions to Alternative Bases
- A Cubic Counterpart of Jacobi's Identity and the AGM
- SOME INEQUALITIES FOR THE GENERALIZED GRÖTZSCH FUNCTION
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