tmp/tmprgw1mlgm/{from.md → to.md}
RENAMED
|
@@ -0,0 +1,17 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
#### Incomplete elliptic integral of the second kind <a id="sf.cmath.ellint_2">[[sf.cmath.ellint_2]]</a>
|
| 2 |
+
|
| 3 |
+
``` cpp
|
| 4 |
+
double ellint_2(double k, double phi);
|
| 5 |
+
float ellint_2f(float k, float phi);
|
| 6 |
+
long double ellint_2l(long double k, long double phi);
|
| 7 |
+
```
|
| 8 |
+
|
| 9 |
+
*Effects:* These functions compute the incomplete elliptic integral of
|
| 10 |
+
the second kind of their respective arguments `k` and `phi` (`phi`
|
| 11 |
+
measured in radians).
|
| 12 |
+
|
| 13 |
+
*Returns:* $$%
|
| 14 |
+
\mathsf{E}(k, \phi) =
|
| 15 |
+
\int_0^\phi \! \sqrt{1 - k^2 \sin^2 \theta} \, \mathsf{d}\theta,
|
| 16 |
+
\quad \mbox{for $|k| \le 1$}$$ where k is `k` and φ is `phi`.
|
| 17 |
+
|