convolutions
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1—10 of 14 matching pages
1: 30.10 Series and Integrals
2: 35.2 Laplace Transform
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Convolution Theorem
►If is the Laplace transform of , , then is the Laplace transform of the convolution , where ►
35.2.3
3: 27.5 Inversion Formulas
4: 2.6 Distributional Methods
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►We now derive an asymptotic expansion of for large positive values of .
►In terms of the convolution product
…The replacement of by its asymptotic expansion (2.6.9), followed by term-by-term integration leads to convolution integrals of the form
…However, the left-hand side can be considered as the convolution of the two distributions associated with the functions and , given by (2.6.12) and (2.6.13).
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►The method of distributions can be further extended to derive asymptotic expansions for convolution integrals:
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5: 7.21 Physical Applications
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►Voigt functions , , can be regarded as the convolution of a Gaussian and a Lorentzian, and appear when the analysis of light (or particulate) absorption (or emission) involves thermal motion effects.
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6: 1.14 Integral Transforms
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Convolution
►For Fourier transforms, the convolution of two functions and defined on is given by … ►Convolution
►For Laplace transforms, the convolution of two functions and , defined on , is … ►Convolution
…7: 2.5 Mellin Transform Methods
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►with .
►One of the two convolution integrals associated with the Mellin transform is of the form
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2.5.3
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2.5.29
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2.5.31
for .
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8: Bibliography G
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Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
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Riccati equations and convolution formulae for functions of Rayleigh type.
J. Phys. A 33 (7), pp. 1363–1368.
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9: Bibliography W
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Explicit error terms for asymptotic expansions of Mellin convolutions.
J. Math. Anal. Appl. 72 (2), pp. 740–756.
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10: Bibliography
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Algorithm 588. Fast Hankel transforms using related and lagged convolutions.
ACM Trans. Math. Software 8 (4), pp. 369–370.
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