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11—20 of 135 matching pages
11: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Theory of Incomplete Cylindrical Functions and Their Applications.
Springer-Verlag, Berlin.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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12: 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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13: 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)). …14: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Comput. Phys. Comm. 99 (2-3), pp. 297–306.
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15: 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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16: 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
…17: 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 …18: 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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19: 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
… ►20: Bibliography C
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Caustics in cylindrical ducts.
Proc. Roy. Soc. London Ser. A 455, pp. 2529–2548.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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