# [Maxima] bessel_i quadpack bug 5.26.0

Raymond Toy toy.raymond at gmail.com
Wed Feb 29 17:07:19 CST 2012

```On Wed, Feb 29, 2012 at 1:38 PM, Edwin Woollett <woollett at charter.net>wrote:

> On Feb. 29, 2012, Raymond Toy wrote:
> -------------------------
>
>  This could probably be fixed by changing how bessel_i(1,%i*x) is computed.
>> bessel_i(1,3*%i) has a small real part >even though we know it must be
>> purely imaginary.
>>
>> For the other bessel functions at %i*x the result is complex, except
>> bessel_j.  For bessel_j, it looks like we are >careful and return a purely
>> imaginary result.
>>
>> Or maybe tell maxima that bessel_i(n,%i*x) = bessel_j(n,x).  Maxima
>> doesn't
>> seem to know that property.  Maybe the >simplifier should honor %iargs to
>> do this transformation.
>>
>
> the relation Mathematica has on page
>
> http://functions.wolfram.com/**Bessel-TypeFunctions/BesselI/**16/01/01/<http://functions.wolfram.com/Bessel-TypeFunctions/BesselI/16/01/01/>
>
> is
>
> bessel_i(nu,%i*z) = (%i*z)^nu * bessel_j(nu,z) / z^nu
>
> but I haven't checked this numerically.
>
>
Yes, I was careless in my original email.  I have implemented this on my
tree and things work as expected.  Still need to make bessel_i(n,%i*float)
return a purely imaginary result, though.  bessel_j apparently already does
this.

Ray
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