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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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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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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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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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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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Generalized Orlicz-Type Slice Spaces, Extrapolation and Applications
We introduce a class of generalized Orlicz-type Auscher—Mourgoglou slice space, which is a special case of the Wiener amalgam. We prove versions of...
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Sharp Approximations for Complete p-Elliptic Integral of the Second Kind by Weighted Power Means
In this paper, the well-known double inequality for the complete elliptic integral E ( r ) of the second kind, which gives sharp approximations of E ( r )...
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Chapter 2 Abelian Integrals and Limit Cycles
In this chapter we will explain the relation between the number of zeros of the Abelian integrals and the number of limit cycles of the corresponding...
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Elliptic Curves over the Rationals
This chapter covers prerequisites on elliptic curves over $$\mathbb...
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Approximate Characteristics of Generalized Poisson Operators on Zygmund Classes
The authors analyze approximate characteristics of generalized Poisson operators on Zygmund classes Z α , with the aim of their further application in...
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Theory of generalized Bessel potential space and functional completion
The article’s objective is to present norms based on weighted Dirichlet integrals in the space of generalized Bessel potentials. The weighted...