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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)





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