Re: Taylor expansion of Jacobi's elliptic functions
- To: mathgroup at smc.vnet.net
- Subject: [mg105940] Re: Taylor expansion of Jacobi's elliptic functions
- From: Emu <samuel.thomas.blake at gmail.com>
- Date: Sun, 27 Dec 2009 02:24:56 -0500 (EST)
- References: <hh68kd$bvh$1@smc.vnet.net>
On Dec 27, 11:09 am, did <didier.o... at hotmail.com> wrote:
> With Mathematica 7 on Mac OS X Leopard
>
> In[1]:= Table[Series[JacobiDN[x, m], {x, 0, n}], {n, 0, 4}]]
>
> Out[1]= {SeriesData[x, 0, {EllipticDump`JacobiSum}, 0, 1, 1],
> SeriesData[
> x, 0, {EllipticDump`JacobiSum}, 0, 2, 1], SeriesData[
> x, 0, {1, 0, Rational[-1, 2] m}, 0, 3, 1], SeriesData[
> x, 0, {1, 0, Rational[-1, 2] m}, 0, 4, 1], SeriesData[
> x, 0, {1, 0, Rational[-1, 2] m, 0, Rational[1, 24] (4 m + m^2)}, 0,
> 5, 1]}
>
> Why Mathematica can't give a meaningfull answer for n=0 and n=1, but =
can for
> n>1?
> (Same problem with JacobiSN and JacobiCN)
Here's the result from version 5.2
In[4]:=$Version
Out[4]="5.2 for Mac OS X x86 (32-bit) (February 24, 2006)"
In[3]:=Table[Series[JacobiDN[x, m], {x, 0, n}], {n, 0, 4}]
Out[3]={1, 1, SeriesData[x, 0, {1, 0, -m/2}, 0, 3, 1], SeriesData[x,
0, {1, 0, -m/2}, 0, 4, 1],
SeriesData[x, 0, {1, 0, -m/2, 0, m/6 + m^2/24}, 0, 5, 1]}