Manuscript Em01-G@5 · Em01-G-v5.tex · section · 3fbfe951

Scalar coefficients, profile moments, and locality

Scalar coefficients, profile moments, and locality · lines 1120–1144

Em01-G@5#eq:scalar-coefficients

Let $f_{j, δ, H} = \partial_{t}^{j} F_{δ, H} (0) / j!$ . Define

U_{j}^{ν} (δ) [A] V_{j}^{ν} (δ) [A] u_{n}^{ν} [A] = \frac{1}{32 π ^{2}} \int ν_{n} \frac{L _{δ} ^{j} f _{j, δ, H}}{e _{δ}} d H, = - \frac{1}{32 π ^{2}} \int ν_{n} \frac{L _{δ} ^{j}}{e _{δ}} [FP_{j} (F_{δ, H}) - f_{j, δ, H} lo g (- L_{δ} + i 0)] d H, = j = 0 \sum^{n} \frac{1}{( n - j )!} \partial_{δ}^{n - j} U_{j}^{ν} (0) [A], v_{n}^{ν} [A] = j = 0 \sum^{n} \frac{1}{( n - j )!} \partial_{δ}^{n - j} V_{j}^{ν} (0) [A] .

Displayed formulas in this passage

Em01-G@5#eq:scalar-coefficients · line 1125
$U_{j}^{ν} (δ) [A] V_{j}^{ν} (δ) [A] u_{n}^{ν} [A] = \frac{1}{32 π ^{2}} \int ν_{n} \frac{L _{δ} ^{j} f _{j, δ, H}}{e _{δ}} d H, = - \frac{1}{32 π ^{2}} \int ν_{n} \frac{L _{δ} ^{j}}{e _{δ}} [FP_{j} (F_{δ, H}) - f_{j, δ, H} lo g (- L_{δ} + i 0)] d H, = j = 0 \sum^{n} \frac{1}{( n - j )!} \partial_{δ}^{n - j} U_{j}^{ν} (0) [A], v_{n}^{ν} [A] = j = 0 \sum^{n} \frac{1}{( n - j )!} \partial_{δ}^{n - j} V_{j}^{ν} (0) [A] .$