Results 1 to 10 of about 1,325 (265)

Monotonicity properties and bounds for the complete p-elliptic integrals [PDF]

Journal of Inequalities and Applications, 2018
We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Ti-Ren Huang, Shen-Yang Tan, Xiao-Yan Ma, Yu-Ming Chu   +3 more
doaj   +2 more sources

Generalized Elliptic Integrals [PDF]

Computational Methods and Function Theory, 2008
32 pages, 4 ...
Matti Vuorinen
exaly   +4 more sources

Extended elliptic-type integrals with associated properties and Turán-type inequalities

Advances in Difference Equations, 2021
Our aim is to study and investigate the family of ( p , q ) $(p, q)$ -extended (incomplete and complete) elliptic-type integrals for which the usual properties and representations of various known results of the (classical) elliptic integrals are ...
Rakesh K. Parmar, Ritu Agarwal, Naveen Kumar, S. D. Purohit   +3 more
doaj   +1 more source

Calculation of integrals in MathPartner

Discrete and Continuous Models and Applied Computational Science, 2021
We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for ...
Gennadi I. Malaschonok, Alexandr V. Seliverstov   +1 more
doaj   +1 more source

Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind

Comptes Rendus. Mathématique, 2020
With the aid of the monotone L’Hôpital rule, the authors verify monotonicity of some functions involving complete $(p,q)$-elliptic integrals of the first kind and the inverse of generalized hyperbolic tangent function, derive several sharp inequalities ...
Wang, Fei, Qi, Feng
doaj   +1 more source

Hyperelliptic Integrals to Elliptic Integrals

Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2023
Consider a hyperelliptic integral $I=\int P/(Q\sqrt{S}) dx$, $P,Q,S\in\mathbb{K}[x]$, with $[\mathbb{K}:\mathbb{Q}]<\infty$. When $S$ is of degree $\leq 4$, such integral can be calculated in terms of elementary functions and elliptic integrals of three kinds $\mathcal{F},\mathcal{E},Π$.
openaire   +3 more sources

ε-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

Journal of High Energy Physics, 2023
In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed
Xuhang Jiang, Xing Wang, Li Lin Yang, Jingbang Zhao   +3 more
doaj   +1 more source

Analytic results for two-loop planar master integrals for Bhabha scattering

Journal of High Energy Physics, 2021
We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equations with canonical bases.
Claude Duhr, Vladimir A. Smirnov, Lorenzo Tancredi   +2 more
doaj   +1 more source

An Elliptic Integral Identity [PDF]

Mathematics of Computation, 1971
The definite integral \[ ∫
openaire   +1 more source

Elfun18 – A collection of MATLAB functions for the computation of elliptic integrals and Jacobian elliptic functions of real arguments

SoftwareX, 2019
We outline a set of MATLAB functions that enable the computation of elliptic integrals and Jacobian elliptic functions for real arguments. The correctness, robustness, efficiency, and accuracy of the functions are discussed in detail.
Milan Batista
doaj   +1 more source