integration
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1: 19.13 Integrals of Elliptic Integrals
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§19.13(i) Integration with Respect to the Modulus
… ►§19.13(ii) Integration with Respect to the Amplitude
…2: Alexander A. Its
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►Current research areas of Its are mathematical physics, special functions, and integrable systems.
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► Novokshënov), published by Springer in 1986, Algebro-geometric Approach to Nonlinear Integrable Problems (with E.
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3: Vadim B. Kuznetsov
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►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.
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4: 9.14 Incomplete Airy Functions
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►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.
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5: Alexander I. Bobenko
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►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.
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6: 32.16 Physical Applications
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Integrable Continuous Dynamical Systems
…7: 36.15 Methods of Computation
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§36.15(iii) Integration along Deformed Contour
… ►§36.15(iv) Integration along Finite Contour
…8: Simon Ruijsenaars
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►His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas.
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9: Funding
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Systems Integration for Manufacturing Applications Program of the Engineering Laboratory (formerly Manufacturing Engineering Laboratory)
10: 9.17 Methods of Computation
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►A comprehensive and powerful approach is to integrate the defining differential equation (9.2.1) by direct numerical methods.
As described in §3.7(ii), to ensure stability the integration path must be chosen in such a way that as we proceed along it the wanted solution grows at least as fast as all other solutions of the differential equation.
…On the remaining rays, given by and , integration can proceed in either direction.
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►In the case of the Scorer functions, integration of the differential equation (9.12.1) is more difficult than (9.2.1), because in some regions stable directions of integration do not exist.
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►In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent (§2.4(iv)).
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