Results 1 to 10 of about 2,451 (241)

Generalized Elliptic-Type Integrals and Generating Functions

Demonstratio Mathematica, 2014
On account of analytical importance or application in certain problems in radiation physics and nuclear technology, several interesting families of elliptic-type integrals were recently studied by many authors.
Chaurasia V. B. L., Singh Yudhveer
doaj   +4 more sources

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   +3 more sources

Semi-integration of certain algebraic expressions [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one
M.I. Qureshi, J. Majid
doaj   +3 more sources

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

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

Approximations related to the complete p-elliptic integrals

Open Mathematics, 2022
In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations ...
Zhong Genhong, Ma Xiaoyan, Wang Fei
doaj   +1 more source

On approximation of functions from the class $L^{\psi}_{\beta, 1}$ by the Abel-Poisson integrals in the integral metric

Karpatsʹkì Matematičnì Publìkacìï, 2022
In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
doaj   +1 more source

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

Journal of High Energy Physics, 2018
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have ...
Johannes Broedel, Claude Duhr, Falko Dulat, Lorenzo Tancredi   +3 more
doaj   +1 more source

Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral

Nuclear Physics B, 2017
We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve.
Christian Bogner, Armin Schweitzer, Stefan Weinzierl   +2 more
doaj   +1 more source