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Currently, I am using a Windows machine with *Mathematica 8*. I noticed a difference in a series expansion of the function `EllipticE[]`

in comparison with a result given by *Mathematica 9* on Linux (which I was using previously).

In *Mathematica 8* on Windows the following input:

```
Series[EllipticE[I c, m], {c, Infinity, 0}] // PowerExpand // FullSimplify
```

produces a warning:

General::ivar: I c is not a valid variable. >>

and the following output (slightly rearranged by me to better fit the browser):

$$-\frac{i\left(6m+\frac{(1+m)}{\sinh^2(c)}\right)}{6\sinh(c)m^{3/2}}-\text{EllipticE}[m]+\frac{m \text{EllipticE}[\frac{1}{m}] + (1-m)\text{EllipticK}[\frac{1}{m}] }{\sqrt{m}}-$$ $$\frac{(1+m \cosh(2 c))\sqrt{\text{Limit}\big[-m\sinh^2(c)~,~i c \to 0\big]}}{\sinh^2(c)2m}$$

Same output as a code:

```
-((I (6 m Csch[c] + (1 + m) Csch[c]^3))/(6 m^(3/2))) -
EllipticE[m] +
(m EllipticE[1/m] - (-1 + m) EllipticK[1/m])/Sqrt[m] -
(((1 + m Cosh[2 c]) Csch[c]^2 Sqrt[Limit[-m Sinh[c]^2, I c -> 0]])/(2 m))
```

Now, in *Mathematica 9* on Linux there was no such warning, and no `Limit`

term appeared. I am confused about how to treat this `Limit`

term, since it might just be a sign of something going terribly wrong in the guts of *Mathematica 8*. Does anyone have an advice on how to proceed? Maybe some of you can evaluate the same series expansion in a different version of *Mathematica* so that we could compare results?

### EDIT

Evaluating instead:

```
Series[EllipticE[c, m], {c, I Infinity, 0}] // PowerExpand // FullSimplify
```

worked as a charm without errors.

1No warnings in version 7 and 9, just in version 8. The output is the same as you have. – b.gates.you.know.what – 2013-03-23T15:55:40.203

1From a strictly mathematical point of view,

`Limit[-m Sinh[c]^2, I c -> 0]`

should be zero... – Federico – 2013-03-23T17:05:22.310