jax.scipy.special.lpmn(m, n, z)[source]#

The associated Legendre functions (ALFs) of the first kind.

  • m (int) – The maximum order of the associated Legendre functions.

  • n (int) – The maximum degree of the associated Legendre function, often called l in describing ALFs. Both the degrees and orders are [0, 1, 2, …, l_max], where l_max denotes the maximum degree.

  • z (Array) – A vector of type float32 or float64 containing the sampling points at which the ALFs are computed.

Return type:

tuple[Array, Array]


A 2-tuple of 3D arrays of shape (l_max + 1, l_max + 1, len(z)) containing the values and derivatives of the associated Legendre functions of the first kind. The return type matches the type of z.

  • TypeError if elements of array z are not in (float32, float64).

  • ValueError if array z is not 1D.

  • NotImplementedError if m!=n.