Re: a function containg MeijerG (limit behavior)

• To: mathgroup at smc.vnet.net
• Subject: [mg73329] Re: a function containg MeijerG (limit behavior)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Mon, 12 Feb 2007 05:06:23 -0500 (EST)
• References: <eqmche\$bf4\$1@smc.vnet.net>

```> Sorry for the inconvenience.

No problem at all!

> The expression 'expr' above is what FunctionExpand[f[x1]] should have returned.

"=2E..Enemy of the good is the better..."

I am sure next edition of Mathematica will not face this problem.

Cheers,

Dimitris Anagnostou

Research Associate
National University of Athens, Greece

=CF/=C7 Bhuvanesh =DD=E3=F1=E1=F8=E5:
> As I recall, there was a Sum issue in 5.2 that caused unexpected Interval results from MeijerG. So the Interval returned by the following input, for example, is incorrect.
>
> FunctionExpand[MeijerG[{{0}, {}}, {{0, 0}, {1/2}}, x]]
>
> For your example, after accounting for the FunctionExpand behavior, I get the following in version 5.2:
>
> In[1]:= expr = Cosh[2*x1]*(CoshIntegral[2*x1] + (Log[(-I)*x1] + Log[I*x1])/2 - Log[x1]) - Log[Abs[x1]] -
>          Sinh[2*x1]*SinhIntegral[2*x1];
>
> In[2]:= Limit[expr, x1->0]
>
> Out[2]= EulerGamma + Log[2]
>
> In[3]:= Series[expr, {x1,0,2}, Assumptions -> 0<x1<1/100] //InputForm
>
> Out[3]//InputForm= SeriesData[x1, 0, {EulerGamma + Log[2], 0, -3 + 2*EulerGamma + 2*Log[2] + 2*Log[x1]}, 0, 3, 1]
>
> In[4]:= Limit[Normal@%, x1->0]
>
> Out[4]= EulerGamma + Log[2]
>
> In[5]:= Limit[expr, x1->Infinity]
>
> Out[5]= -Infinity
>
> The expression 'expr' above is what FunctionExpand[f[x1]] should have returned.
>
> Sorry for the inconvenience.
>
> Bhuvanesh,
> Wolfram Research.

```

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