       problem with the usage or implemetation of EllipticF[x,m] and

• To: mathgroup at smc.vnet.net
• Subject: [mg110344] problem with the usage or implemetation of EllipticF[x,m] and
• From: Luc Roy <luc.rg.roy at gmail.com>
• Date: Sun, 13 Jun 2010 18:53:43 -0400 (EDT)

```FullSimplify[JacobiAmplitude [Series[EllipticF[x, m], {x, 0, 10}], m]]

should give x + O[x]^10 because the two functions are the inverse of
one another.

however it gives

x - (m x^3)/3 + 1/30 m (2 + 3 m) x^5 - 1/630 m (4 + m (39 + 16 m)) x^7
+ ( m (8 + 3 m (120 + 13 m (20 + 3 m))) x^9)/22680

Am I missing something
or
Is there an implementation problem with Mathematica

Note : the usage of series is very important.
I know the following works and that is not what I need to resolve or
understand.
PowerExpand[JacobiAmplitude [EllipticF[x, m], m]]
Answer: x

```

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