Revision #580 → #1346 · back to history
addedLaplace transform (integral definition)6730346b2f0f
addedSimple harmonic oscillator transformedea274befe4a9
addedLaplace transform of f(t)cbed8b228b18
addedLaplace transform of a Borel measure644226fe9f64
addedProbability measure / Dirac delta case1e92d42175bc
addedBilateral Laplace transformc711f6e1f96f
addedUniqueness up to measure zero5af1a9937adb
addedInverse Laplace transform (Bromwich integral)7ebe267073dd
addedLaplace transform as expectationf854d29c05fc
addedRecovering the CDF5974ac461cf0
addedAlgebraic construction of the transformeb70b9ab02f5
addedConvergence condition53fa525813b7
addedAbsolute convergenceeff1fe27410c
addedAbscissa of absolute convergence9fe0fa3a788f
addedAnalyticity in region of absolute convergence4f73949c6ab6
addedConvergence extends to larger half-planeb31b0973c62c
addedIntegration-by-parts representationef6f394e2ab7
addedOne-to-one correspondence with holomorphic functionsb198fff7114f
addedPaley–Wiener theorems8c33a621cdfc
addedLTI stability criterion8abf668a6304
addedDifferentiation/integration to multiplication/division3a281734dc84
addedTable of unilateral transform properties4061f60ffc63
addedFinal value theoremb99433aa9c25
addedContinuous analogue of a power series635eb83090a3
addedAnalyticity analogous to power series6a3e56ec02fe
addedMoments via differentiationdd1828b34f9d
addedDifferentiation property27ffdcdfaca0
addedTransform of n-th derivative9e98f7121991
addedParseval-type integral propertydd8c218af9d0
addedComputing a difficult integral29a7ce8f3324
addedLaplace–Stieltjes transform8f178971fe5d
addedCoincidence with Laplace transform99622201bfe1
addedLaplace transform yields Fourier transform1cd88bed4849
addedFourier as bilateral transform at s=iω2496cd57fbde
addedValidity requires ROC contains imaginary axisf5769df4fb52
addedCosine transform and its ROC0ecd8d277f77
addedMellin–Laplace change of variables6a08f4e6c2e9
addedZ-transform via sampling56e98f1ac13f
addedZ-transform–Laplace relationship0b867e806a6b
addedBorel transformd922eb6e0370
addedNachbin's theoremf1faea0d5aa9
addedUnity of integral transformsd8c96fd65984
addedLinearity (sum)b817fef9cb48
addedLinearity (scalar multiple)64f299571e8a
addedEvaluating improper integralsbedb0110c4cd
addedComplex impedance of a capacitora1f47152bae3
addedImpulse response via partial fractions1aea226582cc
addedPhase delaye44646d58a0f
addedPartition function via Laplace transformaae64ec00631
addedAstronomical spatial structure from spectrumef1aa35e622a
addedBirth and death processes (random walk)8b0881e7ae30
addedTauberian theorems1ddc6455f34c
addedIkehara Tauberian theoremb7d4ffeac83e
addedApplication to prime number theoremca51dbbbd8d2