lpmn#
- scipy.special.lpmn(m, n, z)[source]#
- Sequence of associated Legendre functions of the first kind. - Computes the associated Legendre function of the first kind of order m and degree n, - Pmn(z)= \(P_n^m(z)\), and its derivative,- Pmn'(z). Returns two arrays of size- (m+1, n+1)containing- Pmn(z)and- Pmn'(z)for all orders from- 0..mand degrees from- 0..n.- This function takes a real argument - z. For complex arguments- zuse clpmn instead.- Deprecated since version 1.15.0: This function is deprecated and will be removed in SciPy 1.17.0. Please - scipy.special.assoc_legendre_p_allinstead.- Parameters:
- mint
- |m| <= n; the order of the Legendre function.
- nint
- where - n >= 0; the degree of the Legendre function. Often called- l(lower case L) in descriptions of the associated Legendre function
- zarray_like
- Input value. 
 
- Returns:
- Pmn_z(m+1, n+1) array
- Values for all orders 0..m and degrees 0..n 
- Pmn_d_z(m+1, n+1) array
- Derivatives for all orders 0..m and degrees 0..n 
 
 - See also - clpmn
- associated Legendre functions of the first kind for complex z 
 - Notes - In the interval (-1, 1), Ferrer’s function of the first kind is returned. The phase convention used for the intervals (1, inf) and (-inf, -1) is such that the result is always real. - References [1]- Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html [2]- NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/14.3