       Re: a function containg MeijerG (limit behavior)

• To: mathgroup at smc.vnet.net
• Subject: [mg73312] Re: a function containg MeijerG (limit behavior)
• From: Bhuvanesh <BhuvaneshBhatt at gmail.com>
• Date: Sun, 11 Feb 2007 01:16:06 -0500 (EST)
• Organization: The Math Forum

```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:= 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:= Limit[expr, x1->0]

Out= EulerGamma + Log

In:= Series[expr, {x1,0,2}, Assumptions -> 0<x1<1/100] //InputForm

Out//InputForm= SeriesData[x1, 0, {EulerGamma + Log, 0, -3 + 2*EulerGamma + 2*Log + 2*Log[x1]}, 0, 3, 1]

In:= Limit[Normal@%, x1->0]

Out= EulerGamma + Log

In:= Limit[expr, x1->Infinity]

Out= -Infinity

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

Sorry for the inconvenience.

Bhuvanesh,
Wolfram Research.

```

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