inverse Laplace transform

SearchAdvancedHelp

(0.002 seconds)

1—10 of 23 matching pages

1: 16.20 Integrals and Series

… ►Extensive lists of Laplace transforms and inverse Laplace transforms of the Meijer $G$-function are given in Prudnikov et al. (1992a, §3.40) and Prudnikov et al. (1992b, §3.38). …

2: 19.13 Integrals of Elliptic Integrals

… ►For direct and inverse Laplace transforms for the complete elliptic integrals $K\left(k\right)$, $E\left(k\right)$, and $D\left(k\right)$ see Prudnikov et al. (1992a, §3.31) and Prudnikov et al. (1992b, §§3.29 and 4.3.33), respectively.

3: 2.4 Contour Integrals

… ►For examples and extensions (including uniformity and loop integrals) see Olver (1997b, Chapter 4), Wong (1989, Chapter 1), and Temme (1985). ►

§2.4(ii) Inverse Laplace Transforms

… ►

2.4.7 $$q(t)-f(t)=\frac{{\mathrm{e}}^{\sigma t}}{2\pi }\underset{\eta \to \mathrm{\infty }}{lim}{\int }_{-\eta }^{\eta }{\mathrm{e}}^{\mathrm{i}t\tau }(Q(\sigma +\mathrm{i}\tau )-F(\sigma +\mathrm{i}\tau ))d\tau .$$

ⓘ

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $\mathrm{i}$: imaginary unit, $\int$: integral, $q(t)$: analytic function, $Q(z)$: Laplace transform of $q(t)$ , $\sigma$: constant, $F(z)$: comparison function and $f(x)$: inverse transform of comparison function

Permalink:

http://dlmf.nist.gov/2.4.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §2.4(ii), §2.4 and Ch.2

… ►For examples see Olver (1997b, pp. 315–320). …

4: 15.14 Integrals

… ►Inverse Laplace transforms of hypergeometric functions are given in Erdélyi et al. (1954a, §5.19), Oberhettinger and Badii (1973, §2.18), and Prudnikov et al. (1992b, §3.35). …

5: 16.15 Integral Representations and Integrals

… ►For inverse Laplace transforms of Appell functions see Prudnikov et al. (1992b, §3.40).

6: 16.5 Integral Representations and Integrals

… ►Laplace transforms and inverse Laplace transforms of generalized hypergeometric functions are given in Prudnikov et al. (1992a, §3.38) and Prudnikov et al. (1992b, §3.36). …

7: 24.13 Integrals

… ►For Laplace and inverse Laplace transforms see Prudnikov et al. (1992a, §§3.28.1–3.28.2) and Prudnikov et al. (1992b, §§3.26.1–3.26.2). …

8: 3.11 Approximation Techniques

… ►

Laplace Transform Inversion

►Numerical inversion of the Laplace transform (§1.14(iii)) …

9: 35.2 Laplace Transform

… ►

Inversion Formula

…

10: 10.71 Integrals

… ►For direct and inverse Laplace transforms of Kelvin functions see Prudnikov et al. (1992a, §3.19) and Prudnikov et al. (1992b, §3.19). …