legendre_p(n, x)
where n is the degree of the polynomial. For example, for the Legendre polynomial of the first kind of the 5th degree simply type legendre_p(5, x).
For the Legendre function of the second kind the command is
legendre_q(n, x)
For the associated Legendre functions where there is also an order, m, in addition to the degree, n, to specify. Remember that regular Legendre functions are just associated Legendre functions of order 0.
assoc_legendre_q(n, m, x)
assoc_legendre_q(n, m, x)
Here are some links to these commands and more special functions and orthogonal functions/polynomials.
http://www.ma.utexas.edu/maxima/maxima_16.html
Although this link^ has the regular Legendre function with an order which is not needed. It is listed as
legendre_p(n, m, x)
where it should just be like it is posted above.
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