Re: Integral involving erfc and j1
- To: mathgroup at smc.vnet.net
- Subject: [mg26451] Re: [mg26393] Integral involving erfc and j1
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Thu, 21 Dec 2000 01:51:53 -0500 (EST)
- References: <200012200521.AAA05467@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Rod wrote:
>
> Mathematica fails to solve the following integral
>
> Integrate[Erfc[a x] j1[x]^2/x,{x,0,inf}]
>
> where
>
> j1[x_]=Sqrt[Pi/(2 x)] BesselJ[3/2,x]
>
> How can i make it do the work ?
> --
> __ _
> / / (_)__ __ ____ __
> / /__/ / _ \/ // /\ \/ / . . . t h e c h o i c e o f a
> /____/_/_//_/\_,_/ /_/\_\ G N U g e n e r a t i o n . . .
>
> Sent via Deja.com
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I assume you mean Infinity for 'inf'. I do not know how to make this
work for generic parameter 'a' but for given values you might do as
follows.
In[14]:= ii[a_] := Simplify[Erfc[a*x]*Sqrt[Pi/(2*x)]* BesselJ[3/2,x],
x>=0]
In[17]:= Integrate[ii[3], {x,0,Infinity}]
1
Out[17]= 1 - 3 Sqrt[Pi] Erf[-]
6
Daniel Lichtblau
Wolfram Research
- References:
- Integral involving erfc and j1
- From: Rod <rodolphe6831@my-deja.com>
- Integral involving erfc and j1