fn central<const SLOPE: bool>(
v: f64,
order: i32,
x: f64,
) -> Result<(Scaled, Scaled)>Expand description
(P_ν^{-μ}(x), (1 - x²) dP_ν^{-μ}/dx) from the expansion about x = 0.
P_ν^{-μ}(x) = (1 - x²)^{μ/2} G(x), where G solves
(1 - x²) G'' - 2(μ + 1) x G' + (ν - μ)(ν + μ + 1) G = 0, so its Taylor coefficients obey
g_{j+2} = g_j (j + μ - ν)(j + μ + ν + 1)/((j + 1)(j + 2)); g_0 and g_1 are the value
and slope at zero (DLMF 14.5.1, 14.5.2). With X = x², G = E(X) + x O(X).