Manuscript Em01-D@2 · Em01-D-v2.tex · proposition · d3b49151

Proposition: Profile comparison under the certificate

Support, profiles, admissibility, and output › Fixed-profile versus profile-independent limits · lines 1615–1635 · proof included or linked

Em01-D@2#prop:profiles

For two normalized compact profiles using the same input package,

A_{λ, k}^{ρ} - A_{λ, k}^{ρ} T^{ρ} - T^{ρ} = \frac{1}{k !} H_{λ, J_{λ} - k} [\cdot] (ρ - ρ), = H_{0, J_{0}} [\cdot] (ρ - ρ) .

The second expression is zero if degree zero is absent. It compares finite parts; if the raw families converge, it compares their raw limits.

Proof. Subtract (eq:maincoeff) and (eq:mainfinite). The value $W_{Φ} (0)$ is independent of the profile.

Displayed formulas in this passage

unlabeled · line 1618
$A_{λ, k}^{ρ} - A_{λ, k}^{ρ} T^{ρ} - T^{ρ} = \frac{1}{k !} H_{λ, J_{λ} - k} [\cdot] (ρ - ρ), = H_{0, J_{0}} [\cdot] (ρ - ρ) .$