Manuscript Em02-A@6 · Em02-A-v6.tex · section · cb2f0a9a

Consistency benchmark: explicit complete smooth-data expansion

Consistency benchmark: explicit complete smooth-data expansion · lines 2198–2222

This benchmark is not a singular physical coefficient calculation.

Suppose $C$ is a smooth crossed array near $π (supp ζ)$ , with $χ = 1$ on a larger neighborhood. Any smooth extension agreeing there may be used in the localized formulas. Fix an even normalized $ρ$ and put

M_{α} = \int s^{α} ρ (s) d s, C_{[n]} = ∣ α ∣ = n \sum \frac{( - 1 ) ^{n} M _{α}}{α !} \partial^{α} C .

Odd arrays vanish. Define the complete moment distributions

A_{n}^{ζ} (Φ) = ⟨ T_{C_{[n]}} (K_{ret}), ζ Φ ⟩ .

Their explicit seed actions are given by (eq:exact-raw) with $C_{[n]}$ replacing $c_{δ}$ .

Displayed formulas in this passage

unlabeled · line 2208
$M_{α} = \int s^{α} ρ (s) d s, C_{[n]} = ∣ α ∣ = n \sum \frac{( - 1 ) ^{n} M _{α}}{α !} \partial^{α} C .$
unlabeled · line 2215
$A_{n}^{ζ} (Φ) = ⟨ T_{C_{[n]}} (K_{ret}), ζ Φ ⟩ .$

Consistency benchmark: explicit complete smooth-data expansion

Displayed formulas in this passage

Nearby in this section