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On Generalized Complete (p, q)-Elliptic Integrals
In this paper, we study the generalized complete ( p, q )-elliptic integrals of the first and second kind as an application of generalized...
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ε-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves
In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana...
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An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into...
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Regularized Integrals on Elliptic Curves and Holomorphic Anomaly Equations
We derive residue formulas for the regularized integrals (introduced by Li and Zhou in Commun Math Phys 388:1403–1474, 2021) on configuration spaces...
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Loop-by-loop differential equations for dual (elliptic) Feynman integrals
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We...
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Elliptic integrals
While Lundberg and others found ways to parameterize the p-circle in the late 19th century, mathematicians have thought about using...
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On epsilon factorized differential equations for elliptic Feynman integrals
In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method...
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Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals
In the article, we present the best possible bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals of the...
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New solutions to Legendre’s incomplete elliptic integrals of the first and second kinds and p-elliptic integrals
The elliptic integrals are of interest in various disciplines. While series solutions do exist for complete elliptic integrals, there are no deduced...
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Approximation of Generalized Poisson Integrals by Interpolating Trigonometric Polynomials
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities for 2 π -periodic functions f that can be represented in...
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Generalized Localization and Summability Almost Everywhere of Multiple Fourier Series and Integrals
It is well known that Luzin’s conjecture has a positive solution for one-dimensional trigonometric Fourier series, but in the multidimensional case...
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Integrals
In this chapter, we encounter a rich collection of tantalizing integrals in its 60 sections. The reader is invited to evaluate a broad panel of...
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Two Masses in Relative Hooke’s Potential and Elliptic Integrals
We consider the relative motion of the system of two masses connected by a spring. We analyze it in a range of the Hooke’s law and show that the...
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Duals of Feynman Integrals. Part II. Generalized unitarity
The first paper of this series introduced objects (elements of twisted relative cohomology) that are Poincaré dual to Feynman integrals. We show how...
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Evaluating master integrals in non-factorizable corrections to t-channel single-top production at NNLO QCD
We studied the two-loop non-factorizable Feynman diagrams for the t -channel single-top production process in quantum chromodynamics. We present a...