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MathGroup Archive 1998

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Re: Integrate[Exp[-(1-x)^2]/Sqrt[x],{x,0,Infinity}]



Andrea Bellettini wrote:
> 
> Can someone explain the following behavior?
> 
> In[48]:= $Version
> 
> Out[48]= HP9000 Series 700 2.2 (May 7, 1993)
> 
> In[49]:= Integrate[Exp[-(1-x)^2]/Sqrt[x],{x,0,Infinity}]
> 
> On::none: Message SeriesData::csa not found.
> 
>          I      2          1  1
> Out[49]= - Sqrt[-] BesselK[-, -]
>          2      E          4  2
> 
> In[50]:= N@%
> 
> Out[50]= 0.411862 I
> 
> In[51]:= NIntegrate[Exp[-(1-x)^2]/Sqrt[x],{x,0,Infinity}]
> 
> Out[51]= 1.97373
> 
> What is the meaning of csa?


Andrea:

Message SeriesData::csa not found

means that the message name SeriesData::csa was called but no associated
message was found.

>From the technical report Mathematica Warning Messages it seems that a message 
Argument e in expr is not a power series
is normally generated when at least one of the arguments to ComposeSeries is
not a aeries (expression with head SeriesData).

This apparently shows up a bug - but all is well in Mathematica3.01:


Integrate[Exp[-(1-x)^2]/Sqrt[x],{x,0,Infinity}]

              1   1            1  1
Pi (BesselI[-(-), -] + BesselI[-, -])
              4   2            4  2
-------------------------------------
              2 Sqrt[E]

N[%]

1.97373

NIntegrate[Exp[-(1-x)^2]/Sqrt[x],{x,0,Infinity}]

1.97373

-- 
Allan Hayes
Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642




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