## Sunday, December 25, 2011

### Legendre functions (also associated) of the first and second kind in Maxima

In order to do Legendre functions in Maxima the command is

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.