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1: 19.13 Integrals of Elliptic Integrals

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§19.13(i) Integration with Respect to the Modulus

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§19.13(ii) Integration with Respect to the Amplitude

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2: 37.20 Mathematical Applications

… ►Partial sums of Fourier orthogonal polynomial expansions are polynomials of best approximation in $L^2\left(W\right)$ space and they are also the essential building blocks for approximation in $L^p$ spaces. The $L^2$ norms of the monic OPs are the error of the least square approximation of monomials by polynomials of lower degrees. … ►

Numerical Integration and Interpolation

►A minimal cubature rule is a numerical integration rule that uses the smallest number of nodes among cubature rules of the same degree. …Although Gaussian cubature rules rarely exist and they do not exist for centrally symmetric domains, minimal or near minimal cubature rules on the unit square are known and provide efficient numerical integration rules. …

3: Alexander A. Its

… ►Current research areas of Its are mathematical physics, special functions, and integrable systems. … ► Novokshënov), published by Springer in 1986, Algebro-geometric Approach to Nonlinear Integrable Problems (with E. …

4: Vadim B. Kuznetsov

… ►Kuznetsov published papers on special functions and orthogonal polynomials, the quantum scattering method, integrable discrete many-body systems, separation of variables, Bäcklund transformation techniques, and integrability in classical and quantum mechanics. …

5: 9.14 Incomplete Airy Functions

… ►Incomplete Airy functions are defined by the contour integral (9.5.4) when one of the integration limits is replaced by a variable real or complex parameter. …

6: Alexander I. Bobenko

… ►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E. … Eitner), published by Springer in 2000, and Discrete Differential Geometry: Integrable Structure (with Y. …He is also coeditor of Discrete Integrable Geometry and Physics (with R. …

7: 32.16 Physical Applications

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Integrable Continuous Dynamical Systems

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8: Simon Ruijsenaars

… ►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …

9: Funding

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Systems Integration for Manufacturing Applications Program of the Engineering Laboratory (formerly Manufacturing Engineering Laboratory)

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10: 31.18 Methods of Computation

… ►Independent solutions of (31.2.1) can be computed in the neighborhoods of singularities from their Fuchs–Frobenius expansions (§31.3), and elsewhere by numerical integration of (31.2.1). …Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)). …