1—10 of 14 matching pages
Convolution Theorem►If is the Laplace transform of , , then is the Laplace transform of the convolution , where ►
… ►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). … ►The method of distributions can be further extended to derive asymptotic expansions for convolution integrals: …
… ►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. …
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 … ►
… ►with . ►One of the two convolution integrals associated with the Mellin transform is of the form ►
2.5.3 ,… ►
2.5.31 for .…
Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
Riccati equations and convolution formulae for functions of Rayleigh type.
J. Phys. A 33 (7), pp. 1363–1368.
Explicit error terms for asymptotic expansions of Mellin convolutions.
J. Math. Anal. Appl. 72 (2), pp. 740–756.
Algorithm 588. Fast Hankel transforms using related and lagged convolutions.
ACM Trans. Math. Software 8 (4), pp. 369–370.