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11—20 of 95 matching pages
11: 28.32 Mathematical Applications
12: 20.13 Physical Applications
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βΊThe functions , , provide periodic solutions of the partial differential equation
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20.13.1
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20.13.2
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13: 1.6 Vectors and Vector-Valued Functions
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1.6.19
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1.6.20
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1.6.22
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βΊSuppose is an oriented surface with boundary which is oriented so that its direction is clockwise relative to the normals of .
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βΊwhere is the derivative of normal to the surface outwards from and is the unit outer normal vector.
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14: 3.4 Differentiation
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§3.4(iii) Partial Derivatives
… βΊ … βΊThe results in this subsection for the partial derivatives follow from Panow (1955, Table 10). Those for the Laplacian and the biharmonic operator follow from the formulas for the partial derivatives. … βΊ15: 19.4 Derivatives and Differential Equations
16: 30.13 Wave Equation in Prolate Spheroidal Coordinates
17: 31.10 Integral Equations and Representations
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βΊand the kernel is a solution of the partial differential equation
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31.10.4
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31.10.8
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βΊand the kernel is a solution of the partial differential equation
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31.10.18
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18: 14.11 Derivatives with Respect to Degree or Order
19: 36.12 Uniform Approximation of Integrals
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βΊAlso, is real analytic, and for all such that all critical points coincide.
If , then we may evaluate the complex conjugate of for real values of and , and obtain by conjugation and analytic continuation.
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36.12.2
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36.12.10
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