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. Thanks a lot firstly for your timing and secondly for reply! "=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.