`scipy.special._multiufuncs:assoc_legendre_p`

Signature

   def     assoc_legendre_p (    n    ,    m    ,    z    ,  * ,     branch_cut    =  2   ,    norm    =  False   ,    diff_n    =  0     )

Associated Legendre polynomial of the first kind.

n : ArrayLike[int]: Degree of the associated Legendre polynomial. Must have n >= 0.
m : ArrayLike[int]: order of the associated Legendre polynomial.
z : ArrayLike[float | complex]: Input value.
branch_cut : Optional[ArrayLike[int]]: Selects branch cut. Must be 2 (default) or 3. 2: cut on the real axis |z| > 1 3: cut on the real axis -1 < z < 1
norm : Optional[bool]: If True, compute the normalized associated Legendre polynomial. Default is False.
diff_n : Optional[int]: A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

p : ndarray or tuple[ndarray]: Associated Legendre polynomial with diff_n derivatives.

The normalized counterpart of an (unnormalized) associated Legendre polynomial has the additional factor

\frac{( 2 n + 1 ) ( n - m )!}{2 ( n + m )!}