# term-by-term integration

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## 1—10 of 151 matching pages

##### 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. …##### 6: 32.16 Physical Applications

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###### Integrable Continuous Dynamical Systems

…##### 7: 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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##### 8: Funding

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

##### 9: 31.18 Methods of Computation

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►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)).
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##### 10: 21.9 Integrable Equations

###### §21.9 Integrable Equations

►Riemann theta functions arise in the study of*integrable differential equations*that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). … ►