cylindrical polar coordinates
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11—20 of 49 matching pages
11: 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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12: Bibliography K
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On multiple zeros of derivatives of Bessel’s cylindrical functions.
Dokl. Akad. Nauk SSSR 288 (2), pp. 285–288 (Russian).
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On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions.
Zh. Vychisl. Mat. i Mat. Fiz. 27 (11), pp. 1628–1639, 1758.
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Multiple complex zeros of derivatives of the cylindrical Bessel functions.
Dokl. Akad. Nauk SSSR 299 (3), pp. 614–618 (Russian).
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Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument.
ACM Trans. Math. Software 34 (4), pp. Art. 22, 21.
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Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument.
ACM Trans. Math. Software 37 (4), pp. Art. 47, 25.
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13: 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
…14: 13.28 Physical Applications
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§13.28(i) Exact Solutions of the Wave Equation
►The reduced wave equation in paraboloidal coordinates, , , , can be solved via separation of variables , where …15: 23.21 Physical Applications
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§23.21(iii) Ellipsoidal Coordinates
►Ellipsoidal coordinates may be defined as the three roots of the equation …where are the corresponding Cartesian coordinates and , , are constants. The Laplacian operator (§1.5(ii)) is given by ►
23.21.2
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16: Bibliography M
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Lie theory and separation of variables. I: Parabolic cylinder coordinates.
SIAM J. Math. Anal. 5 (4), pp. 626–643.
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Calculation of zeros of cylindrical functions and their derivatives.
Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).
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Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions.
2nd edition, Springer-Verlag, Berlin.
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17: 30.13 Wave Equation in Prolate Spheroidal Coordinates
§30.13 Wave Equation in Prolate Spheroidal Coordinates
►§30.13(i) Prolate Spheroidal Coordinates
… ►§30.13(ii) Metric Coefficients
… ►§30.13(iii) Laplacian
… ►18: 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 …19: 18.39 Applications in the Physical Sciences
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►where is a spatial coordinate, the mass of the particle with potential energy , is the reduced Planck’s constant, and a finite or infinite interval.
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►Now use spherical coordinates (1.5.16) with instead of , and assume the potential to be radial.
…By (1.5.17) the first term in (18.39.21), which is the quantum kinetic energy operator , can be written in spherical coordinates
as
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