# [Maxima] Maxima can't solve this integral equation

Richard Hennessy rvh2007 at comcast.net
Thu Jun 26 13:01:05 CDT 2008

```Thanks,

I didn't know about that Maxima function.  It works.

Rich

------------Original Message------------
From: "Raymond Toy (RT/EUS)" <raymond.toy at ericsson.com>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Stavros Macrakis" <macrakis at alum.mit.edu>, "Maxima List" <maxima at math.utexas.edu>, "Raymond Toy" <toy.raymond at gmail.com>
Date: Thu, Jun-26-2008 1:40 PM
Subject: Re: [Maxima] Maxima can't solve this integral equation

Richard Hennessy wrote:
> Okay, this was too much to ask but still Maxima was able to help though.  The original input was
>
> sqrt(2)*sqrt(m)*integrate(sqrt(E[n]-mu*x^4),x,-E[n]^(1/4)/mu^(1/4),E[n]^(1/4)/mu^(1/4))=%pi*hbar*(n-1/2);
>
> After using changevar and subst and numeric integration I did finally get
>
> E[n]^(3/4)=((0.57206982262637*%pi*hbar*mu^(1/4)*(n-1/2))/(sqrt(2)*sqrt(m)))
>
> which is right, I hope, or my book is wrong and me too.

FWIW, I think integrate(sqrt(1-z^4),z,-1,1) is 4/3*elliptic_kc(-1).

Ray

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