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From: did on 26 Dec 2009 19:09
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)




From: Emu on 27 Dec 2009 02:28
On Dec 27, 11:09 am, did <didier.o...(a)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]}

From: did on 28 Dec 2009 04:55
On Dec 27, 8:28 am, Emu <samuel.thomas.bl...(a)gmail.com> wrote:
> On Dec 27, 11:09 am, did <didier.o...(a)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.

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