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Re: Bug with LaplaceTransform?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83628] Re: [mg83499] Bug with LaplaceTransform?
  • From: Devendra Kapadia <dkapadia at wolfram.com>
  • Date: Mon, 26 Nov 2007 03:46:45 -0500 (EST)
  • References: <200711210806.DAA06327@smc.vnet.net>

On Wed, 21 Nov 2007, chuck009 wrote:

> The Laplace Transform integral seems not to converge for any s for the function f(x)=1/x but LaplaceTransform returns -EulerGamma-Log(s) for this function:
>
>
> LaplaceTransform[1/x, x, s]
> Integrate[1/(x*Exp[s*x]), {x, 0, Infinity}]
>
> Is this a bug?
>
Hello,

The answer returned by LaplaceTransform in the above example is incorrect 
and this example should return unevaluated.

The problem appears to be caused by the setting GenerateConditions -> 
False with which the integral is computed by LaplaceTransform. With this 
setting, Integrate attempts to regularize the divergent integral. Hence
a workaround for the problem is to use GenerateConditions -> True in
this case, as shown below.

================================

In[1]:= $Version

Out[1]= 6.0 for Linux x86 (32-bit) (June 28, 2007)

In[2]:= LaplaceTransform[1/x, x, s, GenerateConditions -> True] // InputForm

                                1
Integrate::idiv: Integral of ------ does not converge on {0, Infinity}.
                               s x
                              E    x

Out[2]//InputForm= LaplaceTransform[x^(-1), x, s, GenerateConditions -> True]

=============================

Thank you for reporting the problem. We are sorry for the inconvenience
caused by it.

Sincerely,

Devendra Kapadia,
Wolfram Research, Inc.


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