Taylor series of elliptic_kc(m) about m=0 fails with error
Subject: Taylor series of elliptic_kc(m) about m=0 fails with error
From: David Billinghurst
Date: Thu, 20 Sep 2012 19:40:47 +1000
On 20/09/2012 5:53 PM, Aleksas Domarkas wrote:
> From maxima help:
> Function: elliptic_kc (m)
> The complete elliptic integral of the first kind, defined as
> integrate(1/sqrt(1 - m*sin(x)^2), x, 0, %pi/2)
>
> Example 1 Compute taylor(elliptic_kc(m), m, 0, 1)
>
> (%i1) taylor(integrate(1/sqrt(1-m*sin(x)^2),x,0,%pi/2),m,0,1);
> (%o1)/T/ %pi/2+((at(integrate(sin(x)^2,x,0,%pi/2),m=0))*m)/2+...
> (%i2) ev(%,integrate);
> (%o2)/R/ (%pi*m+4*%pi)/8
> (%i3) taylor(%,m,0,1);
> (%o3)/T/ %pi/2+(%pi*m)/8+...
Thanks Aleksas. That agrees with
taylor(hypergeometric([1/2,1/2],[1],m),m,0,5), as it should. It is good
to have confirmation.