### The Maxima on-line user's manual

Algebra Calculator

#### Assoc_legendre_p

Function: assoc_legendre_p (<n>, <m>, <x>) The associated Legendre function of the first kind of degree <n> and order <m>.

Reference: Abramowitz and Stegun, equations 22.5.37, page 779, 8.6.6 (second equation), page 334, and 8.2.5, page 333.

```(%o1)                                true
(%i2) ```

### Related Examples

##### assoc_legendre_p-legendre_p

x:assoc_legendre_p(5,...

Calculate

##### assoc_legendre_p-assoc_legendre_q-diff-legendre_p-legendre_q

f(x):= ((x*x-1)^(-0/2...

f(-%i);

f1(x):=''(diff(f(x),x));

Calculate

##### assoc_legendre_p-assoc_legendre_q-diff-legendre_p-legendre_q

f(x):= ((x*x-1)^(-0/2...

f(-%i);

f1(x):=''(diff(f(x),x));

Calculate

##### legendre_p

legendre_p(3, 0.89);

Calculate

##### assoc_legendre_p-diff-legendre_p

z:assoc_legendre_p(5,...

k:diff(assoc_legendre...

Calculate

legendre_p(3,x);

Calculate

##### assoc_legendre_p-assoc_legendre_q-diff-legendre_p-legendre_q

f(x):= ((x*x-1)^(-0/2...

f1(x):=''(diff(f(x),x));

f1(0);

Calculate

##### assoc_legendre_p-diff-legendre_p

z([x]):= assoc_legend...

z(0);

k([x]):=diff(assoc_le...

Calculate

##### assoc_legendre_p-diff-legendre_p

z([x]):= assoc_legend...

z(0);

k([x]):=diff(assoc_le...

Calculate

##### legendre_p

legendre_p(3, x);

Calculate