       Re: Strange error message from NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg28159] Re: [mg28149] Strange error message from NIntegrate
• From: BobHanlon at aol.com
• Date: Mon, 2 Apr 2001 02:18:29 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```You made the power of x a list (brackets vice parenthreses).

There are still problems with the numerical integration.  However, you can

- approximate the answer with a finite upper limit of integration
- change the number of intervals (GaussPoints)
- change the method of numerical integration

NIntegrate[x^(3/2)*Exp[-x]*BesselI[3/2,x/2], {x,0, 1000}]

1.0030037040845279

NIntegrate[x^(3/2)*Exp[-x]*BesselI[3/2,x/2], {x,0, Infinity},
GaussPoints -> 10]

1.0030037040849122

NIntegrate[x^(3/2)*Exp[-x]*BesselI[3/2,x/2], {x,0, Infinity},
Method -> Trapezoidal]

1.0030037040847963

Bob Hanlon

In a message dated 2001/4/1 1:16:26 AM, h.holm at spray.no writes:

>I am trying to do the following numerical integration:
>
>  NIntegrate[x^{3/2}*Exp[-x]*BesselI[3/2,x/2], {x,0, Infinity}]
>
>this results in the following error,
>
>  NIntegrate::"inum":
>   Integrand {0.141859424324175} is not numerical at {x} = {1.}.
>
>I think this is very strange, after all, 0.1418... _is_ a
>number.  It might be noted that doing the integration
>symbolically works nicely:
>
>  Integrate[x^{3/2}*Exp[-x]*BesselI[3/2,x/2], {x,0, Infinity}]
>
>which gives the following result:
>
>  16/(9*Sqrt[pi])
>
>
>I guess I am doing something wrong, but I cannot understand
>what.  Can anybody help me?
>

```

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