AFLegendre¶
-
pylayers.antprop.spharm.AFLegendre(N, M, x)[source]¶ calculate Pmm1n and Pmp1n
- Nint
max order (theta) (also called l or level )
- Mint
max degree (phi)
- xnp.array
function argument
Pmm1l : ndarray ( Ndir, M , L )
\(\bar{P}_{n}^{(m-1)}(x)\)
- Pmp1lndarray ( Ndir, M , L )
\(\bar{P}_{n}^{(m+1)}(x)\)
- This function returns :
- \[ \begin{align}\begin{aligned}\bar{P}_{l}^{(m-1)}(x)\\\bar{P}_{l}^{(m+1)}(x)\end{aligned}\end{align} \]
Where
\[P_l^{(m)}(x)= \sqrt{ \frac{2}{2 l+1} \frac{(l+m)!}{(l-m)!} } \bar{P}_{l}^{(m)}(x)\]
>>> Pmm1n,Pmp1n = AFLegendre(5,4,np.array([0,1]))
VW