Manuscript XVI-K@1 · XVI-K.tex · section · aa7553bb

Basis and independent jets

The declared density and its full jet Hessian › Basis and independent jets · lines 637–653

XVI-K@1#eq:jetdefinition

For a fully finite specification, let $L ((g_{i, r})_{∣ r ∣ \leq 2})$ be the jet polynomial obtained from (eq:Gamma)–(eq:ell3). Then

L^{pq}_{ij} (w; h) = \frac{\partial ^{2} L}{\partial g _{i, p} \partial g _{j, q}}_{g_{a, r} = \partial^{r} h^{a} (w)} .

This specifies every coefficient without an external table. No extra factorial is associated with a mixed derivative jet.

Displayed formulas in this passage

XVI-K@1#eq:jetdefinition · line 642
$L^{pq}_{ij} (w; h) = \frac{\partial ^{2} L}{\partial g _{i, p} \partial g _{j, q}}_{g_{a, r} = \partial^{r} h^{a} (w)} .$