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Mathematica vs Alpha output in Laplace transformation?

Posted 3 months ago
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I am learning my way around Mathematica. Using simple problems with known solutions I find that the output from Mathematica (V10) and alpha sometimes differ in the way they are presented, or rather Alpha provides more options.

For example computing the Laplace Transform, in Mathematica, of

LaplaceTransform[t^2 UnitStep[t - a], t, s]

yields

(E^(-a s) (2 E^(a s) UnitStep[-a] + 2 UnitStep[a] + 
   2 a s UnitStep[a] + a^2 s^2 UnitStep[a]))/s^3

while using Alpha returns alternate forms, including enter image description here

How do I get Mathematica to output the alternate forms?

2 Replies

As it seems Wolfram|Alpha is assuming a>0. Try e.g.:

ltf = LaplaceTransform[t^2 UnitStep[t - a], t, s];
Refine[ltf, a > 0]
PiecewiseExpand[ltf]
Posted 3 months ago

Thanks. Refine works as hoped for. Using Expand, rather than PiecewiseExpand yields the same result.

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