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Assoc_legendre_q

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

Alpha:1;
Fr:sqrt(2);
y:-%i*((4.0*(Alpha+1)/(Fr*Fr))-1)^(-0.5)*x;
y: x;
f(x):= (1-x^2)^(-Alpha/2)*assoc_legendre_q(8,-1,x);
plot2d(realpart(f(y)),[x,0.1,1]);

Reference: Abramowitz and Stegun, equation 8.5.3 and 8.1.8.

(%o1)                                true
(%i2) 

Related Examples

assoc_legendre_q-legendre_q-plot2d-realpart-sqrt
plot2d(realpart(f(x)),[x,0.2,0.5]);

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-plot2d-realpart-sqrt
plot2d(realpart(f(y)),[x,0.8,1.0]);

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-numer-realpart-sqrt

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-plot2d-realpart-sqrt
plot2d(realpart(f(y)),[x,0.1,0.5]);

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-plot2d-realpart-sqrt
plot2d(realpart(f(y)),[x,0,1]);

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-numer-realpart-sqrt

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-numer-realpart-sqrt

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate

assoc_legendre_q-legendre_q-plot2d-realpart-sqrt
plot2d(realpart(f(y)),[x,0.01,1.0]);

Alpha:1;

Fr:sqrt(2);

y:-%i*((4.0*(Alpha+1)...

Calculate