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The link from Maxima's assoc_legendre_p to Sage's gen_legendre_p will be done by ticket #16813 (among many other things). Until then you must do manually sage: assoc_legendre_p = gen_legendre_P sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n() ... TypeError: no conversion of this rational to integer which however shows that Maxima itself cannot handle the function with non-integer index. Using the branch in the ticket gives sage: assoc_legendre_p = gen_legendre_P sage: sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n() -0.483843755630126 + 0.369716687246133*I

The link from Maxima's assoc_legendre_p to Sage's gen_legendre_p will be done by ticket #16813 (among many other things). Until then you must do manually manually

 sage: assoc_legendre_p = gen_legendre_P
sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
...
TypeError: no conversion of this rational to integer

 sage: assoc_legendre_p = gen_legendre_P
sage: sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
-0.483843755630126 + 0.369716687246133*I

The link from Maxima's assoc_legendre_p to Sage's gen_legendre_p will be done by ticket #16813 (among many other things). Until then you must do manually

sage: assoc_legendre_p = gen_legendre_P
sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
...
TypeError: no conversion of this rational to integer

which however shows that Maxima itself cannot handle the function with non-integer index. Using the branch in the ticket gives

sage: assoc_legendre_p = gen_legendre_P
sage: sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
-0.483843755630126 + 0.369716687246133*I

The link from Maxima's assoc_legendre_p to Sage's gen_legendre_pgen_legendre_P will be done by ticket #16813 (among many other things). Until then you must do manually

sage: assoc_legendre_p = gen_legendre_P
sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
...
TypeError: no conversion of this rational to integer

which however shows that Maxima itself cannot handle the function with non-integer index. Using the branch in the ticket gives

sage: assoc_legendre_p = gen_legendre_P
sage: print (-1/2*sqrt(3)*assoc_legendre_p(1/2, -1, -5/3)).n()
-0.483843755630126 + 0.369716687246133*I