kernel equations
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1—10 of 24 matching pages
1: 31.10 Integral Equations and Representations
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Kernel Functions
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31.10.8
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Kernel Functions
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31.10.18
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►leads to the kernel equation
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2: 28.10 Integral Equations
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§28.10(i) Equations with Elementary Kernels
… ►§28.10(ii) Equations with Bessel-Function Kernels
…3: 28.28 Integrals, Integral Representations, and Integral Equations
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§28.28(i) Equations with Elementary Kernels
…4: 18.2 General Orthogonal Polynomials
5: 28.32 Mathematical Applications
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►Kernels
can be found, for example, by separating solutions of the wave equation in other systems of orthogonal coordinates.
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6: 10.63 Recurrence Relations and Derivatives
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►Equations (10.63.6) and (10.63.7) also hold when the symbols and in (10.63.5) are replaced throughout by and , respectively.
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7: 10.68 Modulus and Phase Functions
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►Equations (10.68.8)–(10.68.14) also hold with the symbols , , , and replaced throughout by , , , and , respectively.
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8: Errata
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Equations (18.2.12), (18.2.13)
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18.2.12
18.2.13
The left-hand sides were updated to include the definition of the Christoffel–Darboux kernel .
9: 10.61 Definitions and Basic Properties
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►When suffices on , , , and are usually suppressed.
►Most properties of , , , and follow straightforwardly from the above definitions and results given in preceding sections of this chapter.
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§10.61(ii) Differential Equations
… ►10: 13.27 Mathematical Applications
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►The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions.
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►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i).