Manuscript XIV-E@1 · XIV-E.tex · section · e89fd2a5

The first calculation: the entire six-branch sum

E1: exact calculation of the complete precomposition sum › The first calculation: the entire six-branch sum · lines 640–660

XIV-E@1#eq:CG, XIV-E@1#eq:Btensor

Define the smooth coefficient

C_{G}^{μ}_{ν} = f \partial_{ν} X_{G}^{μ} - δ^{μ}_{ν} \partial_{ρ} (f X_{G}^{ρ}),

and the complete tensor

B^{α μ} [G; h] = a_{1}^{α β} [h] \partial_{β} X_{G}^{μ} + a_{1}^{α β} [G] \partial_{β} X_{h}^{μ} + a_{2} ˙^{α μ} [G; h] + a_{1}^{α μ} [r_{h}] .

Displayed formulas in this passage

XIV-E@1#eq:CG · line 643
$C_{G}^{μ}_{ν} = f \partial_{ν} X_{G}^{μ} - δ^{μ}_{ν} \partial_{ρ} (f X_{G}^{ρ}),$
XIV-E@1#eq:Btensor · line 650
$B^{α μ} [G; h] = a_{1}^{α β} [h] \partial_{β} X_{G}^{μ} + a_{1}^{α β} [G] \partial_{β} X_{h}^{μ} + a_{2} ˙^{α μ} [G; h] + a_{1}^{α μ} [r_{h}] .$