Re: Taylor expansion of Jacobi's elliptic functions
- To: mathgroup at smc.vnet.net
- Subject: [mg105955] Re: Taylor expansion of Jacobi's elliptic functions
- From: did <didier.oslo at hotmail.com>
- Date: Mon, 28 Dec 2009 04:55:12 -0500 (EST)
- References: <hh68kd$bvh$1@smc.vnet.net> <hh72b4$kt0$1@smc.vnet.net>
On Dec 27, 8:28 am, Emu <samuel.thomas.bl... at gmail.com> wrote:
> On Dec 27, 11:09 am, did <didier.o... at hotmail.com> wrote:
>
>
>
>
>
> > With Mathematica 7 on Mac OS X Leopard
>
> > In[1]:= Table[Series[JacobiDN[x, m], {x, 0, n}], {n, 0, 4}]]
>
> > Out[1]= {SeriesData[x, 0, {EllipticDump`JacobiSum}, 0, 1, 1],
> > SeriesData[
> > x, 0, {EllipticDump`JacobiSum}, 0, 2, 1], SeriesData[
> > x, 0, {1, 0, Rational[-1, 2] m}, 0, 3, 1], SeriesData[
> > x, 0, {1, 0, Rational[-1, 2] m}, 0, 4, 1], SeriesData[
> > x, 0, {1, 0, Rational[-1, 2] m, 0, Rational[1, 24] (4 m + m^2)}, 0,
> > 5, 1]}
>
> > Why Mathematica can't give a meaningfull answer for n=0 and n=1, bu=
t =
> can for
> > n>1?
> > (Same problem with JacobiSN and JacobiCN)
>
> Here's the result from version 5.2
>
> In[4]:=$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]}
It looks OK. So, there is a bug in Mathematica 7.