SatelliteToolboxLegendre.jl

Associated Legendre functions and derivatives with multiple normalization options. Repo: JuliaSpace/SatelliteToolboxLegendre.jl

Computing Legendre Functions

# P[n+1, m+1] = P_{n,m}[cos(ϕ)]
P = legendre(Val(:full), ϕ, n_max)                    # Full normalization
P = legendre(Val(:schmidt), ϕ, n_max, m_max)          # Schmidt semi-normalization
P = legendre(Val(:unnormalized), ϕ, n_max)            # Unnormalized

# In-place (zero-allocation)
legendre!(Val(:full), P, ϕ, n_max, m_max)

Computing Derivatives

(dP, P) = dlegendre(Val(:full), ϕ, n_max)             # Returns both dP and P
dlegendre!(dP, ϕ, P, n_max, m_max)                     # In-place (P must be pre-computed)

Key Conventions

• First argument N selects normalization: Val(:full), Val(:schmidt), Val(:unnormalized)
• Angle ϕ in radians
• Indexing: P[n+1, m+1] for degree n, order m
• Optional ph_term=true includes Condon-Shortley phase (-1)^m
• In-place variants infer n_max/m_max from matrix dimensions if omitted
• Zero external dependencies (pure Julia)