Results 1 to 10 of about 1,712 (185)
Generalized Elliptic-Type Integrals and Generating Functions [PDF]
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
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Elliptic Feynman integrals and pure functions [PDF]
Journal of High Energy Physics, 2019 We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term.
Johannes Broedel +4 more
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Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism [PDF]
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 +3 more
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Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms [PDF]
, 2019 We describe algorithms to compute elliptic functions and their relatives (Jacobi theta functions, modular forms, elliptic integrals, and the arithmetic-geometric mean) numerically to arbitrary precision with rigorous error bounds for arbitrary complex variables. Implementations in ball arithmetic are available in the open source Arb library. We discuss
Fredrik Johansson, Johansson, Fredrik
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Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind [PDF]
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
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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
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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
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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 +1 more
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Hyperelliptic Integrals to Elliptic Integrals [PDF]
, 2023 International audienceConsider a hyperelliptic integral , , with . When S is of degree ≤ 4, such integral can be calculated in terms of elementary functions and elliptic integrals of three kinds .
Combot, Thierry
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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 +3 more
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