tmp/tmpi83m4vjn/{from.md → to.md}
RENAMED
|
@@ -0,0 +1,23 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
#### Associated Legendre functions <a id="sf.cmath.assoc_legendre">[[sf.cmath.assoc_legendre]]</a>
|
| 2 |
+
|
| 3 |
+
``` cpp
|
| 4 |
+
double assoc_legendre(unsigned l, unsigned m, double x);
|
| 5 |
+
float assoc_legendref(unsigned l, unsigned m, float x);
|
| 6 |
+
long double assoc_legendrel(unsigned l, unsigned m, long double x);
|
| 7 |
+
```
|
| 8 |
+
|
| 9 |
+
*Effects:* These functions compute the associated Legendre functions of
|
| 10 |
+
their respective arguments `l`, `m`, and `x`.
|
| 11 |
+
|
| 12 |
+
*Returns:* $$%
|
| 13 |
+
\mathsf{P}_\ell^m(x) =
|
| 14 |
+
(1 - x^2) ^ {m/2}
|
| 15 |
+
\:
|
| 16 |
+
\frac{ \mathsf{d} ^ m}
|
| 17 |
+
{ \mathsf{d}x ^ m} \, \mathsf{P}_\ell(x),
|
| 18 |
+
\quad \mbox{for $|x| \le 1$}$$ where l is `l`, m is `m`, and x is
|
| 19 |
+
`x`.
|
| 20 |
+
|
| 21 |
+
*Remarks:* The effect of calling each of these functions is
|
| 22 |
+
*implementation-defined* if `l >= 128`.
|
| 23 |
+
|