4

The complete elliptic integral of the second kind, `EllipticE`

, is defined as,

```
Integrate[Sqrt[1-m Sin[t]^2],{t,0,z}]
```

According to the version 8 docs, the first of the "Possible Issues" is supposed to evaluate `Integrate[Sqrt[1-m Sin[t]^2],{t,0,z}]`

as

```
If[(m Sin[z]^2 \[NotElement] Reals ||
Re[m Sin[z]^2] <= 1) && (Csc[z]^2/m \[NotElement] Reals ||
Re[Csc[z]^2/m] <= 0 || Re[Csc[z]^2/m] >= 1) &&
2 + m Cos[2 z] != m,
EllipticE[z, m],
Integrate[Sqrt[1 - m Sin[t]^2], {t, 0, z}, Assumptions ->
2 + m Cos[2 z] == m || (((2 - m + m Cos[2 z]) Csc[z]^2)/m \[Element] Reals && -2 <
Re[((2 - m + m Cos[2 z]) Csc[z]^2)/m] < 0) || (Re[m Sin[z]^2] >
1 && m Sin[z]^2 \[Element] Reals)]]
```

whereas I get simply

```
EllipticE[z,m]
```

Is this a bug in the docs?

Same here on 8.0.4/Win7-64 – Sjoerd C. de Vries – 2012-01-30T20:36:19.910

You can always submit any issues you find with the documentation to support@wolfram.com. – Searke – 2012-01-31T21:24:28.600

@Searke Done. :) – JxB – 2012-01-31T22:13:31.263