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Re: factorial and Gamma function

• To: mathgroup at smc.vnet.net
• Subject: [mg77128] Re: factorial and Gamma function
• From: roland franzius <roland.franzius at uos.de>
• Date: Mon, 4 Jun 2007 03:54:21 -0400 (EDT)
• Organization: Universitaet Hannover
• References: <f3u56o$435$1@smc.vnet.net>

dimitris wrote:
> In[23]:= Gamma[1 + t] == t! // FunctionExpand
> Out[23]= True
> 
> In[26]:= FunctionExpand[n!]
> Out[26]= Gamma[1 + n]
> 
> In[27]:=
> LaplaceTransform[t^n, t, s]
> Out[27]=
> s^(-1 - n)*Gamma[1 + n]
> 
> I wanted as output s^(-1 - n)*n!
> 
> Must I define a rule for this or is there a workaround
> using a built in function setting like FullSimplify/FunctionExpand?


Assuming[n > 0 && n \[Element] Integers,
  LaplaceTransform[t^n, t, s] // FullSimplify]

-- 

Roland Franzius