inversion problem

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1: Bibliography X

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Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.

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Notes:

Special issue to celebrate Pierre Sabatier’s 65th birthday (Montpellier, 2000)

External Links:

ISSN 0266-5611, Document, MathReview (Thomas Sauer), ZentralBlatt

Referenced by:

§30.13(v).

Encodings:

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2: 20.9 Relations to Other Functions

… ►The relations (20.9.1) and (20.9.2) between $k$ and $\tau$ (or $q$) are solutions of Jacobi’s inversion problem; see Baker (1995) and Whittaker and Watson (1927, pp. 480–485). …

3: 31.16 Mathematical Applications

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§31.16(i) Uniformization Problem for Heun’s Equation

… ► thesis “Inversion problem for a second-order linear differential equation with four singular points”. …

4: 20.11 Generalizations and Analogs

… ►This is Jacobi’s inversion problem of §20.9(ii). … ►Each provides an extension of Jacobi’s inversion problem. …

5: 10.73 Physical Applications

… ►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging. …

6: 23.22 Methods of Computation

… ►The determination of suitable generators $2{\omega }_1$ and $2{\omega }_3$ is the classical inversion problem (Whittaker and Watson (1927, §21.73), McKean and Moll (1999, §2.12); see also §20.9(i) and McKean and Moll (1999, §2.16)). …

7: Bibliography K

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

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8: 18.40 Methods of Computation

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§18.40(ii) The Classical Moment Problem

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9: 22.19 Physical Applications

… ►Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5). …

10: 2.8 Differential Equations with a Parameter

… ►For another approach to these problems based on convergent inverse factorial series expansions see Dunster et al. (1993) and Dunster (2001a, 2004). …