Poisson%20kernels
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11—20 of 134 matching pages
11: 1.8 Fourier Series
12: Bibliography H
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Asymptotic expansion of a class of integral transforms with algebraically dominated kernels.
J. Math. Anal. Appl. 35 (2), pp. 405–433.
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Solutions of Poisson’s equation in channel-like geometries.
Comput. Phys. Comm. 115 (1), pp. 45–68.
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13: 19.18 Derivatives and Differential Equations
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►and also a system of
Euler–Poisson differential equations (of which only are independent):
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►The next four differential equations apply to the complete case of and in the form (see (19.16.20) and (19.16.23)).
►The function satisfies an Euler–Poisson–Darboux equation:
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14: 18.12 Generating Functions
15: 10.62 Graphs
16: 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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17: 8 Incomplete Gamma and Related
Functions
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18: 28 Mathieu Functions and Hill’s Equation
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19: 31.10 Integral Equations and Representations
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Kernel Functions
… ►The kernel must satisfy … ►Kernel Functions
… ►The kernel must satisfy … ►leads to the kernel equation …20: 10.67 Asymptotic Expansions for Large Argument
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§10.67(i) , and Derivatives
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10.67.1
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►The contributions of the terms in , , , and on the right-hand sides of (10.67.3), (10.67.4), (10.67.7), and (10.67.8) are exponentially small compared with the other terms, and hence can be neglected in the sense of Poincaré asymptotic expansions (§2.1(iii)).
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10.67.14
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10.67.15
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