Taylor expansion of Jacobi's elliptic functions
- To: mathgroup at smc.vnet.net
- Subject: [mg105925] Taylor expansion of Jacobi's elliptic functions
- From: did <didier.oslo at hotmail.com>
- Date: Sat, 26 Dec 2009 19:07:20 -0500 (EST)
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)