Manuscript XVI-O1-ST@5 · XVI-O1-ST-v5.tex · proposition · dd45e0d1

Proposition: Variation count and derivative

Retained gauge-pole data and exact printed consequences · lines 1452–1468 · proof included or linked

XVI-O1-ST@5#prop:derivative, XVI-O1-ST@5#eq:hhderivative

Exactly 13 of these 14 structures vary with $ξ$ ; $B_{14}$ is constant. The printed derivative is

b_{hh} (ξ) = j \sum (a_{j}^{(1)} + 2 (ξ - 1) a_{j}^{(2)}) B_{j} .

These facts do not require correcting either version of $f$ .

Proof. Only row 14 has both variable coefficients zero. Differentiate the finite polynomial.

Displayed formulas in this passage

XVI-O1-ST@5#eq:hhderivative · line 1457
$b_{hh} (ξ) = j \sum (a_{j}^{(1)} + 2 (ξ - 1) a_{j}^{(2)}) B_{j} .$