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When I insert the following integration command in wolframalpha:

int(pi^2*0.05*Exp[-0.1]*14142135/2*x^-1*
  Exp[-x]*y*Exp[-pi*0.1*y^2/2]*
  Hypergeometric2F1[1, 2/3, 5/3, -2*y^-4*(2*10^14)^(3/4)]*
  BesselI[2, x*y*Sqrt[2*pi]],{x,0,0.25},{y,0,Infinity})

I get the following numerical result 6.68805

However, inserting the same command in Mathematica as follows:

NIntegrate[pi^2*0.05*Exp[-0.1]*14142135/2*x^-1*
  Exp[-x]*y*Exp[-pi*0.1*y^2/2]*
  Hypergeometric2F1[1,2/3,5/3,-2*y^-4*(2*10^14)^(3/4)]*
  BesselI[2,x*y*Sqrt[2*pi]],{x,0,0.25},{y,0,Infinity}]

I get the following output (no result)

enter image description here

Am I doing something wrong in Mathematica? Does the wolframalpha site has extended functionality compared to Mathematica (in the above concept).

Thanks in advance

PS: I suppose that wolfralpha translates int() as NIntegrate in the specific case.

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5  
My eyes got pain, plz Latex :-) –  Babak S. May 16 '13 at 15:37
1  
To anyone thinking about editing this: Please do not merely substitute plaintext with LaTeX. This question is asking about outputs of Mathematica and WolframAlpha and it will do answerers no good to have only the pretty LaTeX without having something they too can put into these programs to replicate the error. –  Eric Stucky May 16 '13 at 15:50
    
@Eric: This is why I have expressed my question in this form. Thank you for your kind comment. And of course I am very sorry for my big and ugly expression, yet, this is what I am looking for. –  dioxen May 16 '13 at 15:51
    
What happens if you use $int$ in both cases? My guess is that the code uses different algorithms and branches within those algorithm. You can certainly use integrate in both cases, but I do not believe you can use nintegrate in WA. –  Amzoti May 16 '13 at 16:48
    
Eric is correct that it doesn't make a lot of sense to input this as LaTeX. I think it does make sense to type it in as code, however. This is very easily accomplished by simply indenting your code block four spaces, as I've done in my edit. –  Mark McClure May 17 '13 at 15:37

1 Answer 1

up vote 6 down vote accepted

I think the apparent answer to your problem is that you entered in Mathematica:

NIntegrate[pi^2 ... blah ]

... and in Mathematica, Pi is the exact real number $\pi$ = 3.1415 ... but pi is just a name like cat or mouse. Capital letters matter. Wolfram Alpha is more flexible about such things, perhaps because it needs to be. This explains why you would get the message about your expression not being numerical, because it contains a pi (or a cat or a dog).

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Indeed, if you replace pi by Pi, Mathematica 8 spits out the numerical answer. –  MathJJ May 16 '13 at 17:38
    
Thank you wolfies, the answer is simple and the result indeed derived. Until now, mathematica translated pi as Pi for simpler expressions. –  dioxen May 16 '13 at 21:07

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