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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-legendre_p

assoc_legendre_p(10,6...

Calculate

assoc_legendre_p-legendre_p

assoc_legendre_p(15,7...

Calculate

assoc_legendre_p-legendre_p

assoc_legendre_p(5,1,...

Calculate

assoc_legendre_p-diff-legendre_p

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

z(0);

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

Calculate

assoc_legendre_p-legendre_p

assoc_legendre_p(10,7...

Calculate

assoc_legendre_p-legendre_p

assoc_legendre_p(10,7...

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assoc_legendre_p-assoc_legendre_q-diff-legendre_p-legendre_q

f(x):= assoc_legendre...

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

f1(0);

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):= assoc_legendre...

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

f1(0);

Calculate

assoc_legendre_p

Run Example
(%i1)z:assoc_legendre_p(5,0,x);
                               5              4                            2
                     63 (1 - x)    315 (1 - x)              3   105 (1 - x)
(%o1) - 15 (1 - x) - ----------- + ------------ - 70 (1 - x)  + ------------
                          8             8                            2
                                                                            + 1
(%i2) k:diff(assoc_legendre_p(5,0,x),x);
                                   4              3
                        315 (1 - x)    315 (1 - x)               2
(%o2)   - 105 (1 - x) + ------------ - ------------ + 210 (1 - x)  + 15
                             8              2
(%i3) 
Run Example
? 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) 
Run Example
assoc_legendre_p(10,10,.5);
(%o1)         interval(1.5537027854003906E+8, 10.72027973934915)
(%i2) 

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