Notes on the complete elliptic integral of the first kind
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Publication:5108658
DOI10.7153/mia-2020-23-07zbMath1440.33020OpenAlexW3005189011MaRDI QIDQ5108658
Wei-Mao Qian, Wen Zhang, Zhen-Hang Yang, Yu-Ming Chu
Publication date: 5 May 2020
Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.7153/mia-2020-23-07
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
- Monotonicity of the incomplete gamma function with applications
- Optimal combinations bounds of root-square and arithmetic means for Toader mean
- Dynamics analysis of a class of delayed economic model
- Optimal inequalities between harmonic, geometric, logarithmic, and arithmetic-geometric means
- 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
- A new analysis of electrostatic free energy minimization and Poisson-Boltzmann equation for protein in ionic solvent
- A power mean inequality involving the complete elliptic integrals
- Inequalities for \(\alpha\)-fractional differentiable functions
- Monotonicity rule for the quotient of two functions and its application
- Numerical solution of the Goursat problem on a triangular domain with mixed boundary conditions
- A new globalization technique for nonlinear conjugate gradient methods for nonconvex minimization
- A class of logarithmically completely monotonic functions associated with a gamma function
- Logarithmically complete monotonicity properties relating to the gamma function
- On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function
- Inequalities between arithmetic-geometric, Gini, and Toader means
- Convexity of the complete elliptic integrals of the first kind with respect to Hölder means
- A modified Perry's conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations
- Monotonicity theorems and inequalities for the complete elliptic integrals
- Integral inequalities involving strongly convex functions
- Optimal bounds for Gaussian arithmetic-geometric mean with applications to complete elliptic integral
- Ostrowski type inequalities involving conformable fractional integrals
- Optimal bounds for the generalized Euler-Mascheroni constant
- Sharp bounds for the Sándor-Yang means in terms of arithmetic and contra-harmonic means
- Hermite-Hadamard type inequalities for fractional integrals via Green's function
- Quadratic transformation inequalities for Gaussian hypergeometric function
- Inequalities and infinite product formula for Ramanujan generalized modular equation function
- Conformable fractional integrals versions of Hermite-Hadamard inequalities and their generalizations
- A PRP-based residual method for large-scale monotone nonlinear equations
- Generalization of Hermite-Hadamard type inequalities via conformable fractional integrals
- Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters
- Dynamics of a class of delayed reaction-diffusion systems with Neumann boundary condition
- Some new inequalities of Hermite-Hadamard type for \(s\)-convex functions with applications
- Dynamical behaviors of a food-chain model with stage structure and time delays
- Attractor and boundedness of switched stochastic Cohen-Grossberg neural networks
- On the analysis and application of an ion size-modified Poisson-Boltzmann equation
- On \(A\)-stable one-leg methods for solving nonlinear Volterra functional differential equations
- On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
- Refinements of transformation inequalities for zero-balanced hypergeometric functions
- The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
- Optimal Lehmer mean bounds for the Toader mean
- Spectral collocation methods for Volterra-integro differential equations with noncompact kernels
- Stochastic synchronization of reaction-diffusion neural networks under general impulsive controller with mixed delays
- High accuracy asymptotic bounds for the complete elliptic integral of the second kind
- The general inner-outer iteration method based on regular splittings for the PageRank problem
- Periodic attractor for reaction-diffusion high-order Hopfield neural networks with time-varying delays
- Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term
- Discrete majorization type inequalities for convex functions on rectangles
- On approximating the quasi-arithmetic mean
- Schur \(m\)-power convexity of generalized geometric Bonferroni mean involving three parameters
- Majorization theorems for strongly convex functions
- Improvements of bounds for the Sándor-Yang means
- Association of Jensen's inequality for \(s\)-convex function with Csiszár divergence
- Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
- Monotonicity, convexity and inequalities involving the generalized elliptic integrals
- Sharp bounds for the arithmetic-geometric mean
- Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type
- Integral majorization type inequalities for the functions in the sense of strong convexity
- The concept of coordinate strongly convex functions and related inequalities
- Sharp power mean bounds for two Sándor-Yang means
- Precise estimates for the solution of Ramanujan's generalized modular equation
- Monotonicity criterion for the quotient of power series with applications
- Generalized Lyapunov-Razumikhin method for retarded differential inclusions: applications to discontinuous neural networks
- On rational bounds for the gamma function
- On approximating the Toader mean by other bivariate means
- An optimal power mean inequality for the complete elliptic integrals
- On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities
- Hermite-Hadamard-Fejér inequalities for conformable fractional integrals via preinvex functions
- Conformable integral inequalities of the Hermite-Hadamard type in terms of GG- and GA-convexities
- Sharp Landen transformation inequalities for hypergeometric functions, with applications
- Plasmon resonance and heat generation in nanostructures
- Existence and global attractivity of almost periodic solutions for a delayed differential neoclassical growth model
- Sharp bounds for the Toader-Qi mean in terms of harmonic and geometric means
- Hölder mean inequalities for the complete elliptic integrals
- Asymptotic Expansion of the First Elliptic Integral
- Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
- Some Inequalities for the Growth of Elliptic Integrals
- Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
- 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
- Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting
- Periodic orbit analysis for the delayed Filippov system
- Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion function
- Monotonicity and inequalities involving zero-balanced hypergeometric function
- Stability and Hopf Bifurcation of a Delayed Prey–Predator Model with Disease in the Predator
- On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance
- Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation
- NOTE FOR THE TRIPLED AND QUADRUPLE FIXED POINTS OF THE MIXED MONOTONE MAPPINGS
- Existence of an extinction wave in the Fisher equation with a shifting habitat
- Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems
- Monotonicity properties and bounds for the complete \(p\)-elliptic integrals