convolution%20product
(0.003 seconds)
1—10 of 253 matching pages
1: 30.10 Series and Integrals
…
►For product formulas and convolutions see Connett et al. (1993).
…For expansions in products of spherical Bessel functions, see Flammer (1957, Chapter 6).
2: 27.5 Inversion Formulas
…
►If a Dirichlet series generates , and generates , then the product
generates
►
27.5.1
►called the Dirichlet product (or convolution) of and .
…
►
27.5.8
…
3: 2.6 Distributional Methods
…
►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:
…
4: Bibliography G
…
►
Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
…
►
Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
…
►
Recurrence relations for cross-products of Bessel functions.
Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
…
►
On the exceptional zeros of cross-products of derivatives of spherical Bessel functions.
Z. Angew. Math. Phys. 36 (3), pp. 491–494.
…
►
Riccati equations and convolution formulae for functions of Rayleigh type.
J. Phys. A 33 (7), pp. 1363–1368.
…
5: Bibliography
…
►
Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
…
►
Integrals of products of Bernoulli polynomials.
J. Math. Anal. Appl. 381 (1), pp. 10–16.
…
►
Integrals of products of Airy functions.
J. Phys. A 10 (4), pp. 485–490.
…
►
Algorithm 588. Fast Hankel transforms using related and lagged convolutions.
ACM Trans. Math. Software 8 (4), pp. 369–370.
…
►
An integral of products of ultraspherical functions and a -extension.
J. London Math. Soc. (2) 33 (1), pp. 133–148.
…
6: 27.15 Chinese Remainder Theorem
…
►The Chinese remainder theorem states that a system of congruences , always has a solution if the moduli are relatively prime in pairs; the solution is unique (mod ), where is the product of the moduli.
…
►Their product
has 20 digits, twice the number of digits in the data.
…These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits.
…
7: Bibliography W
…
►
Reduction formulae for products of theta functions.
J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
…
►
The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
…
►
The generalised product moment distribution in samples from a normal multivariate population.
Biometrika 20A, pp. 32–52.
…
►
Explicit error terms for asymptotic expansions of Mellin convolutions.
J. Math. Anal. Appl. 72 (2), pp. 740–756.
…
8: 35.2 Laplace Transform
…
►
Convolution Theorem
►If is the Laplace transform of , , then is the Laplace transform of the convolution , where ►
35.2.3
9: 2.5 Mellin Transform Methods
…
►with .
►One of the two convolution integrals associated with the Mellin transform is of the form
…
►In the half-plane , the product
has a pole of order two at each positive integer, and
…
►
2.5.29
…
►
2.5.31
for .
…
10: Bibliography L
…
►
An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
…
►
Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
…
►
Error bounds for asymptotic expansions of Laplace convolutions.
SIAM J. Math. Anal. 25 (6), pp. 1537–1553.
…
►
A note on the computation of integrals involving products of trigonometric and Bessel functions.
Math. Comp. 27 (124), pp. 871–872.
…
►
Evaluating infinite integrals involving products of Bessel functions of arbitrary order.
J. Comput. Appl. Math. 64 (3), pp. 269–282.
…