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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-diff-legendre_p

z:assoc_legendre_p(5,...

diff(assoc_legendre_p...

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assoc_legendre_p-legendre_p

assoc_legendre_p(10,5...

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assoc_legendre_p-legendre_p

assoc_legendre_p(5,3,...

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assoc_legendre_p-diff-legendre_p

z:assoc_legendre_p(5,...

k:diff(assoc_legendre...

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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);

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assoc_legendre_p-legendre_p

assoc_legendre_p(10,1...

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assoc_legendre_p-legendre_p

assoc_legendre_p(10,7...

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assoc_legendre_p-legendre_p

assoc_legendre_p(4,3,...

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assoc_legendre_p

Run Example
(%i1)F1(x):=assoc_legendre_p(6,-1,x);
(%o1)                F1(x) := assoc_legendre_p(6, - 1, x)
(%i2) DiffF1(x):= ''(diff(F1(x), x));
(%o2) DiffF1(x) := 
                           4              3              2
                165 (1 - x)    165 (1 - x)    225 (1 - x)                  2
(- 60 (1 - x) + ------------ - ------------ + ------------ + 10) sqrt(1 - x )
                     8              2              2
-----------------------------------------------------------------------------
                                      2
                              5              4             3
                    33 (1 - x)    165 (1 - x)    75 (1 - x)              2
 - ((- 10 (1 - x) - ----------- + ------------ - ----------- + 30 (1 - x)  + 1)
                         8             8              2
                 2
 x)/(2 sqrt(1 - x ))
(%i3) a:DiffF1(0),numer;
(%o3)                               0.3125
(%i4) C2:float(a);
(%o4)                               0.3125
(%i5) 
Run Example
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) 

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