Re: definite integral bug (3.0)
- To: mathgroup@smc.vnet.net
- Subject: [mg12104] Re: definite integral bug (3.0)
- From: Bill Bertram <wkb@ansto.gov.au>
- Date: Sat, 25 Apr 1998 01:30:35 -0400
- Organization: ANSTO
- References: <6hjslb$2pd@smc.vnet.net>
Richard Easther wrote:
>
> Hi - I recently tried to persuade Mathematica to do the following
> definite integral,
>
> Integrate[ Exp[-x^2] 1/(1 + Exp[ x]),{x,0,Infinity}]
>
> and it gives the answer
>
> Log[x] 1 + Log[x]
> PolyGamma[0, 1 + ------] - PolyGamma[0, ----------]
> 2 2
> ---------------------------------------------------
> 2
>
This is most disturbing! Whereas for a one off integral of this kind one
could use NIntegate rather than Integrate, if one needed to define a
function of z as,
f[z_]:=Integrate[ Exp[-( z t)^2] /(1 + Exp[t]),{t,0,Infinity}]
to evaluate this for different values of z, then there is a problem. For
example evaluation of f[2] yields,
1/2*(-PolyGamma[0, 1/2 + 2*Log[t]] +
PolyGamma[0, 1 + 2*Log[t]])
This is clearly rubbish and must indicate a bug in this version of
Mathematica.
On the other hand the simpler function,
g[z_]:=Integrate[ Exp[-( z t)^2] ,{t,0,Infinity}]
is OK, eg g[3] -> Sqrt[Pi}/6.
Cheers,
Bill