Subject: Maxima can't solve this integral equation
From: Raymond Toy (RT/EUS)
Date: Thu, 26 Jun 2008 13:40:39 -0400
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