sphero-conal%20coordinates
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1: 29.18 Mathematical Applications
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§29.18(i) Sphero-Conal Coordinates
… ►when transformed to sphero-conal coordinates : … ►
29.18.4
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29.18.5
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29.18.6
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2: 36.5 Stokes Sets
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►For , the Stokes set is expressed in terms of scaled coordinates
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36.5.7
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36.5.10
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►With coordinates
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36.5.17
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3: 20 Theta Functions
Chapter 20 Theta Functions
…4: 12.17 Physical Applications
§12.17 Physical Applications
… ►in Cartesian coordinates of three-dimensional space (§1.5(ii)). By using instead coordinates of the parabolic cylinder , defined by … ►In a similar manner coordinates of the paraboloid of revolution transform the Helmholtz equation into equations related to the differential equations considered in this chapter. … …5: 26.2 Basic Definitions
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►A k-dimensional lattice path is a directed path composed of segments that connect vertices in so that each segment increases one coordinate by exactly one unit.
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6: 14.31 Other Applications
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§14.31(i) Toroidal Functions
… ►§14.31(ii) Conical Functions
►The conical functions appear in boundary-value problems for the Laplace equation in toroidal coordinates (§14.19(i)) for regions bounded by cones, by two intersecting spheres, or by one or two confocal hyperboloids of revolution (Kölbig (1981)). … ►Many additional physical applications of Legendre polynomials and associated Legendre functions include solution of the Helmholtz equation, as well as the Laplace equation, in spherical coordinates (Temme (1996b)), quantum mechanics (Edmonds (1974)), and high-frequency scattering by a sphere (Nussenzveig (1965)). …7: 28.27 Addition Theorems
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►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems.
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8: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14 Wave Equation in Oblate Spheroidal Coordinates
►§30.14(i) Oblate Spheroidal Coordinates
►Oblate spheroidal coordinates are related to Cartesian coordinates by … ►§30.14(ii) Metric Coefficients
… ►§30.14(iii) Laplacian
…9: 13.28 Physical Applications
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