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Mathematica vs Alpha output in Laplace transformation?

Posted 2 years ago

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?

POSTED BY: Ted Bartlett
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 BY: Henrik Schachner
Posted 2 years ago

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

POSTED BY: Ted Bartlett
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