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21—30 of 135 matching pages
21: 28.32 Mathematical Applications
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§28.32(i) Elliptical Coordinates and an Integral Relationship
►If the boundary conditions in a physical problem relate to the perimeter of an ellipse, then elliptical coordinates are convenient. … ► ►§28.32(ii) Paraboloidal Coordinates
►The general paraboloidal coordinate system is linked with Cartesian coordinates via …22: 14.30 Spherical and Spheroidal Harmonics
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►As an example, Laplace’s equation in spherical coordinates (§1.5(ii)):
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►Here, in spherical coordinates, is the squared angular momentum operator:
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23: 8 Incomplete Gamma and Related
Functions
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24: 28 Mathieu Functions and Hill’s Equation
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25: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
26: 23 Weierstrass Elliptic and Modular
Functions
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27: 32.6 Hamiltonian Structure
28: 14.19 Toroidal (or Ring) Functions
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§14.19(i) Introduction
… ►This form of the differential equation arises when Laplace’s equation is transformed into toroidal coordinates , which are related to Cartesian coordinates by …29: 31.17 Physical Applications
30: 36 Integrals with Coalescing Saddles
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