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
> http://www.deja.com/

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

```

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