fn log_series<const SINGULAR: bool, const REGULAR: bool>(
v: f64,
y: f64,
frac_cot: f64,
) -> Result<OrderZero>Expand description
OrderZero from the logarithmic expansion about y = 1 in s = (1 - y)/2:
P_ν = Σ q_k, Q_ν = ½ Σ q_k (c_k - ln s) with q_k = (ν+1)_k (-ν)_k s^k/(k!)² and
c_k = 2ψ(k+1) - ψ(ν+k+1) - ψ(ν+1-k), with the slopes selected as in Sums.
From k = n + 1 (n = ⌊ν⌋) on, q_k carries the factor n - ν = -f, which is split off
(q_k = -f q̂_k) and cancelled analytically against the pole of ψ(ν + 1 - k):
f ψ(f) = f ψ(1 + f) - 1 at k = n + 1, and DLMF 5.5.4, ψ(ν+1-k) = ψ(k-ν) - π cot(πν),
beyond (frac_cot = f π cot(πν)). The digamma updates (DLMF 5.5.2) share one division per
term.