Manuscript XIX-A@1 · XIX-A.tex · section · e30d8062

The relational scalar is not the coordinate map

The finite-time harmonic relational scalar › The relational scalar is not the coordinate map · lines 391–404

XIX-A@1#eq:rel-scalar

For a formal scalar

T_{e} = T_{0} + e θ_{1} + \frac{e ^{2}}{2} θ_{2},

define

R_{H} [q_{e}, T_{e}] := T_{e} \circ H_{q_{e}}^{- 1} .

The inverse is formal, so no global numerical convergence of a perturbation series is asserted.

Displayed formulas in this passage

XIX-A@1#eq:rel-scalar · line 398
$R_{H} [q_{e}, T_{e}] := T_{e} \circ H_{q_{e}}^{- 1} .$
unlabeled · line 394
$T_{e} = T_{0} + e θ_{1} + \frac{e ^{2}}{2} θ_{2},$