In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable...

In mathematics, the inverse Laplace transform of a function F ( s ) {\displaystyle F(s)} is a real function f ( t ) {\displaystyle f(t)} that is piecewise-continuous...

following is a list of Laplace transforms for many common functions of a single variable. The Laplace transform is an integral transform that takes a function...

Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment-generating function. Two-sided Laplace transforms...

representation. It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). This similarity is explored in the theory...

Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform....

probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of...

mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the s-domain. The Laplace transform can be...

Mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided Laplace transform. This integral transform is...

Hankel transform Hartley transform Laplace transform Least-squares spectral analysis Linear canonical transform List of Fourier-related transforms Mellin...

Borel measure on the real line is of this kind. One can define the Laplace transform of a finite Borel measure μ on the real line by the Lebesgue integral...

system's transfer function, which is the Laplace transform of the system's impulse response (or Z transform in the case of discrete-time systems). As...

distributions. The Laplace transform of the Heaviside step function is a meromorphic function. Using the unilateral Laplace transform we have: H ^ ( s )...

f ( t ) {\displaystyle f(t)} in continuous time has (unilateral) Laplace transform F ( s ) {\displaystyle F(s)} , then a final value theorem establishes...

integral transforms like the Hankel transform and the Laplace transform and their inverses result when suitable G-function pairs are employed as transform kernels...

like the Fourier transform. The major difference is that the Laplace transform has a region of convergence for which the transform is valid. This implies...

poles and zeros of the Laplace transform in the complex plane. (In discrete time, one can similarly consider the Z-transform of the impulse response...

frequency domain. Employing the inverse transform, i.e., the inverse procedure of the original Laplace transform, one obtains a time-domain solution. In...

delta (in this formula, its derivative appears). The single-sided Laplace transform of R(x) is given as follows, L { R ( x ) } ( s ) = ∫ 0 ∞ e − s x R...

}^{+\infty }{g(\omega )\ e^{i\ \omega \ t}\ \mathrm {d} \ \omega }} The Laplace transform is another integral operator and is involved in simplifying the process...

improper definite integral can be determined in several ways: the Laplace transform, double integration, differentiating under the integral sign, contour...

viewpoint=[path=M]); Laplace transform f := (1+A*t+B*t^2)*exp(c*t); ( 1 + A t + B t 2 ) e c t {\displaystyle \left(1+A\,t+B\,t^{2}\right)e^{ct}} inttrans:-laplace(f, t...

which the inverse Mellin transform, or equivalently the inverse two-sided Laplace transform, are defined and recover the transformed function. If φ ( s )...

f(t)} and g ( t ) {\displaystyle g(t)} with bilateral Laplace transforms (two-sided Laplace transform) F ( s ) = ∫ − ∞ ∞ e − s u   f ( u )   d u {\displaystyle...

In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications...

_{p}{\frac {\theta _{p}-\theta _{q}}{\theta _{q}}}.\end{aligned}}} The Laplace transform of the gamma PDF, which is the moment-generating function of the gamma...

dividing the Laplace transform of the output, Y ( s ) = L { y ( t ) } {\displaystyle Y(s)={\mathcal {L}}\left\{y(t)\right\}} , by the Laplace transform of the...

} The Laplace transform is the fractional Laplace transform when θ = 90 ∘ . {\displaystyle \theta =90^{\circ }.} The inverse Laplace transform corresponds...

the Laplace transform is found in Doetsch's 1937 work Theorie und Anwendung der Laplace-Transformation (transl. Theory and application of the Laplace transformation)...

Laplace transform can be defined for functions on time scales, which uses the same table of transforms for any arbitrary time scale. This transform can...